CINXE.COM

Introduction to Algebra

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"/></a><div 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aria-label="breadcrumb: Mathematics and Science" class="breadcrumb-item"><a class="text-primary" href="/courses/math-and-science/mathematics-and-science">Mathematics and Science</a></li><li aria-label="breadcrumb: Introduction to Algebra" class="breadcrumb-item text-dark active" aria-current="page">Introduction to Algebra</li></ol></nav></div></div><div class="bg-e2gdark text-white mb-0 jumbotron jumbotron-fluid"><div class="container"><div class="row"><div class="mb-3 col-md-5"><picture><source type="image/webp"/><img class="img-fluid"/></picture></div><div class="col-md-7"><h1>Introduction to Algebra</h1><div data-testid="banner-description"><div><p>Develop a rich understanding of math while you study algebra in a relaxed and supportive environment. This course emphasizes practical math applications of your new algebra skills to help you learn math reasoning in a real-world context and discover solutions to almost any math problem.</p></div></div><div class="justify-content-between row"><div class="col-lg-auto order-lg-last"><div class="py-2"><div class="small d-lg-inline-block py-2">SHARE</div><a aria-label="Share this product with Facebook" href="https://www.facebook.com/sharer/sharer.php?u=https://www.ed2go.com/courses/math-and-science/mathematics-and-science/ilc/algebra-introduction"><svg xmlns="http://www.w3.org/2000/svg" viewBox="-10 -6 38 38"><path d="M10.6 20v-8.5h2.9l.4-3.3h-3.3V6.1c0-1 .3-1.6 1.6-1.6H14v-3c-.3 0-1.3-.1-2.6-.1-2.5 0-4.3 1.5-4.3 4.4v2.4H4.3v3.3h2.9V20h3.4z" fill="#fff"></path></svg></a><a aria-label="Share this product with Twitter" href="https://www.twitter.com/share?url=https://www.ed2go.com/courses/math-and-science/mathematics-and-science/ilc/algebra-introduction"><svg xmlns="http://www.w3.org/2000/svg" viewBox="-10 -6 38 38"><path d="M16.7 6.6c.5 7.9-8.4 12.8-14.9 8.8 1.8 0 3.8-.5 4.9-1.5-1.6-.3-2.7-1-3.1-2.4.5 0 1.1.1 1.4-.1-1.4-.5-2.6-1.4-2.6-3.3.5.1.8.4 1.4.3-.9-.6-2-2.9-1-4.5 1.7 1.9 3.8 3.3 7.1 3.6-.9-3.6 3.8-5.7 5.8-3.2.8-.2 1.5-.5 2.2-.8-.3.8-.9 1.3-1.4 1.8.6-.1 1.3-.2 1.7-.5-.1.7-1 1.3-1.5 1.8z" fill="#fff"></path></svg></a></div><div class="border-bottom border-white d-lg-none"></div></div><div class="col"><div class="row"><div class="col"><div class="d-lg-inline-block py-2 pr-2"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 28 28" aria-label="duration icon" class="text-white"><path d="M14 7c-3.9 0-7 3.1-7 7s3.1 7 7 7 7-3.1 7-7-3.1-7-7-7zm0 16c-5 0-9-4-9-9s4-9 9-9 9 4 9 9-4 9-9 9z"></path><path d="M14 9c-.6 0-1 .4-1 1v4l2.3 2.3c.4.4 1 .4 1.4 0l.1-.1c.4-.4.4-1 0-1.4L15 13v-3c0-.6-.4-1-1-1z"></path></svg><span class="pl-1">6 Weeks / 24 Course Hrs</span></div><div class="d-lg-inline-block py-2 pr-2"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 28 28" aria-label="enrollment status icon" class="text-white"><path d="M20 7h-3c0-1.7-1.3-3-3-3s-3 1.3-3 3H8c-1.1 0-2 .9-2 2v12c0 1.1.9 2 2 2h12c1.1 0 2-.9 2-2V9c0-1.1-.9-2-2-2zm-6-1c.6 0 1 .4 1 1s-.4 1-1 1-1-.4-1-1 .4-1 1-1zm6 15H8V9h2v1h8V9h2v12z"></path><path d="M17 14h-6c-.6 0-1-.4-1-1s.4-1 1-1h6c.6 0 1 .4 1 1s-.4 1-1 1zM17 18h-6c-.6 0-1-.4-1-1s.4-1 1-1h6c.6 0 1 .4 1 1s-.4 1-1 1z"></path></svg><span class="pl-1">Starting  December 18, 2024</span></div></div></div><div class="border-bottom border-white d-md-none"></div></div></div></div></div></div></div><div id="enrollment-section" class="no-gutters enrollment bg-e2g_enrollment text-white row"><div class="container"><div class="row"><div class="col-lg-5 px-3 pt-5 pb-0"><div class="text-uppercase">Offered in partnership with your preferred school</div><h2 class="h5 pt-2">ed2go</h2><div><button aria-label="Why this school?" type="button" class="align-baseline border-0 p-0 text-decoration-none btn btn-link"><span class="mr-3 e2g-enrollment_tooltip">Why this school?</span></button><a class="e2g-enrollment_change-schools" href="/online-schools?product=ita&amp;returnUrl=/courses">Change School</a></div></div><div class="col-lg-7 px-3 py-5"><div class="mb-5 border-bottom border-white d-md-none border-bottom border-white"></div><div class="text-uppercase">Learning method</div><p class="affirm-as-low-as" data-page-type="product" data-amount="18500"></p><label class="mt-2 w-100" for="/enrollment/addtocart.aspx?item=T9316!classes"><div class="checked e2g-enrollment_learning-method p-3"><div class="row px-2"><div class="col-sm-7"><div class="row"><div class="align-items-center col-1 d-flex justify-content-center px-3"><input type="radio" aria-label="Self-Guided" checked="" id="/enrollment/addtocart.aspx?item=T9316!classes" name="enrollment-option" value="/enrollment/addtocart.aspx?item=T9316!classes"/></div><div class="col pl-2 pr-0"><div class="font-weight-bold">Self-Guided</div><div class="font-weight-bold">$185</div><div class="small">No instructor. Study on your own schedule</div></div></div></div><div class="align-self-center col pt-3 pt-sm-0"><div class="align-items-center col-sm d-flex e2g-enroll_btn justify-content-center p-0"><a href="/enrollment/addtocart.aspx?item=T9316!classes" id="checked-enrollment-btn" class="font-weight-bold px-5 text-uppercase btn btn-success">Enroll Now</a></div></div></div></div></label><label class="mt-2 w-100" for="/enrollment/addtocart.aspx?item=ita!classes!1224"><div class="e2g-enrollment_learning-method p-3"><div class="row px-2"><div class="col-sm-7"><div class="row"><div class="align-items-center col-1 d-flex justify-content-center px-3"><input type="radio" aria-label="Instructor-Moderated" id="/enrollment/addtocart.aspx?item=ita!classes!1224" name="enrollment-option" value="/enrollment/addtocart.aspx?item=ita!classes!1224"/></div><div class="col pl-2 pr-0"><div class="font-weight-bold">Instructor-Moderated</div><div class="font-weight-bold">$170</div><div class="small">Confirm your start date in cart</div><div class="small">Starting  December 18 | January 15</div></div></div></div><div class="align-self-center col pt-3 pt-sm-0"><div class="align-items-center col-sm d-flex e2g-enroll_btn justify-content-center p-0"></div></div></div></div></label></div></div></div></div><div class="sticky-top d-none d-md-block" data-testid="desktop-and-tablet-sticky-nav"><div style="height:170px;margin-top:-170px" class="d-none bg-e2g_enrollment container-fluid"><div class="h-100 container"><div class="h-100 row"><div class="align-self-center col-lg-9 col-md-8"><h2 class="font-weight-normal text-white">Introduction to Algebra</h2></div><div class="align-self-center col"><a href="#enrollment-section" class="mb-1 w-100 font-weight-bold px-5 text-uppercase btn btn-success">Enroll Now</a></div></div></div></div><div><nav aria-label="sections" data-testid="section-nav" class="bg-white border-bottom d-none d-md-block section-nav shadow-sm navbar navbar-expand navbar-light"><div class="justify-content-center container"><ul class="flex-wrap font-weight-bold justify-content-around small text-uppercase w-75 navbar-nav"><li class="nav-item"><a href="#objectives" data-rb-event-key="#objectives" class="text-dark nav-link">Details + Objectives</a></li><li class="nav-item"><a href="#outline" data-rb-event-key="#outline" class="text-dark nav-link">Outline</a></li><li class="nav-item"><a href="#instructors" data-rb-event-key="#instructors" class="text-dark nav-link">Instructors &amp; Support</a></li><li class="nav-item"><a href="#requirements" data-rb-event-key="#requirements" class="text-dark nav-link">Requirements</a></li><li class="nav-item"><a href="#faq" data-rb-event-key="#faq" class="text-dark nav-link">FAQ</a></li><li class="nav-item"><a href="#testimonial" data-rb-event-key="#testimonial" class="text-dark nav-link">Reviews</a></li><li class="nav-item"><a href="#relatedCourses" data-rb-event-key="#relatedCourses" class="text-dark nav-link">Related Courses</a></li></ul></div></nav></div></div><div class="objectives py-5" data-dom-id="objectives"><div class="container"><div class="border-bottom border-dark mb-4 pb-3"><h2 class="font-weight-light sticky-nav-target" id="objectives">Details + Objectives</h2><h3 class="font-weight-light">Course code: ita</h3></div><div><p>This online math course integrates mathematics, specifically algebra with many other areas of study, including history, biology, and geography. You will develop a rich understanding of math while you study algebra right here in a relaxed and supportive learning environment. Its emphasis on practical math applications of your new-found algebraic skills will help you learn math reasoning in a real-world context. As a result, you will acquire a wide variety of basic math skills that will help you find solutions to almost any math problem.</p> <p>This concise and straightforward course will help you understand some of the most important mathematical concepts of algebra: order of operations, units of measurement, scientific notation, algebraic equations, rational numbers, and fundamental concepts of accounting like calculating simple interest.</p> <p>By the time you finish this online math course, you will understand how algebra is relevant to every aspect of your daily life!</p><p><strong>What you will learn</strong></p> <ul> <li>Learn definitions, numeric properties, and basic operations</li> <li>Gain and understanding of algebraic concepts: order of operations, units of measurement, scientific notation, algebraic equations, rational numbers and more</li> <li>Acquire a variety of math skills to solve almost any math problem</li> <li>Learn to use your new found math skills in a variety of practical ways</li> </ul> <p><strong>How you will benefit</strong></p> <ul> <li>Obtain a wide variety of math skills that will help you find solutions to almost any math problem</li> <li>Understand the most important mathematical concepts of algebra</li> <li>Gain an understanding of how algebra is relevant in your daily life</li> </ul> <p><strong>How the course is taught</strong></p> <ul> <li>Instructor-Moderated or Self-Guided online course</li> <li>6 Weeks or 3 Months access</li> <li>24 course hours</li> </ul> </div></div></div><div class="bg-light expandable-section py-5" data-dom-id="outline"><div class="container"><div class="border-bottom border-dark mb-4 pb-3"><h2 class="font-weight-light sticky-nav-target" id="outline">Outline</h2></div><button aria-expanded="false" type="button" class="px-0 text-decoration-none text-primary btn btn-link">Expand All</button><button aria-expanded="false" type="button" class="collapsed d-flex font-weight-bold px-0 text-decoration-none text-primary btn btn-link"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 10 10" class="collapse-flip size-1 text-muted mt-1"><path fill="none" stroke="currentColor" stroke-linecap="round" stroke-miterlimit="10" d="M1 3l4 4 4-4"></path></svg><div class="pl-2 text-left">Algebra: Here to Make Life Simpler</div></button><div class="ml-1 pl-4 collapse"><p><span>Your first lesson introduces Al-jabru, the Arabic word for algebra that means the science of restoration and canceling. You will search for algebraic solutions and learn some definitions, numeric properties, and basic operations that originated from the ancient lands where papyrus was used instead of paper.</span></p></div><button aria-expanded="false" type="button" class="collapsed d-flex font-weight-bold px-0 text-decoration-none text-primary btn btn-link"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 10 10" class="collapse-flip size-1 text-muted mt-1"><path fill="none" stroke="currentColor" stroke-linecap="round" stroke-miterlimit="10" d="M1 3l4 4 4-4"></path></svg><div class="pl-2 text-left">How Do You Measure Up?</div></button><div class="ml-1 pl-4 collapse"><p><span>How do calories contribute to weight gain? You will answer this and other questions in this lesson. You will learn the different physical quantities, their units of measurement, and why they're important. You will also learn the difference between mass and weight, and density and weight density.</span></p></div><button aria-expanded="false" type="button" class="collapsed d-flex font-weight-bold px-0 text-decoration-none text-primary btn btn-link"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 10 10" class="collapse-flip size-1 text-muted mt-1"><path fill="none" stroke="currentColor" stroke-linecap="round" stroke-miterlimit="10" d="M1 3l4 4 4-4"></path></svg><div class="pl-2 text-left">Evaluation Time Again</div></button><div class="ml-1 pl-4 collapse"><p><span>This lesson focuses on evaluation, but not the type of evaluation your boss might give you. You will learn about algebraic expressions by using the order of operations and the distributive property translation. You will also practice translating word problems into numerical ones.</span></p></div><button aria-expanded="false" type="button" class="collapsed d-flex font-weight-bold px-0 text-decoration-none text-primary btn btn-link"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 10 10" class="collapse-flip size-1 text-muted mt-1"><path fill="none" stroke="currentColor" stroke-linecap="round" stroke-miterlimit="10" d="M1 3l4 4 4-4"></path></svg><div class="pl-2 text-left">Formula: Another Name for Equation</div></button><div class="ml-1 pl-4 collapse"><p><span>In this lesson, you will learn formulas for basic shapes: squares and rectangles, triangles, circles, spheres, cylinders, and cubes. You may be thinking, "Is this also a geometry course?" In a way you're correct&mdash;some aspects of geometry involve formulas, which people use in everyday life.</span></p></div><button aria-expanded="false" type="button" class="collapsed d-flex font-weight-bold px-0 text-decoration-none text-primary btn btn-link"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 10 10" class="collapse-flip size-1 text-muted mt-1"><path fill="none" stroke="currentColor" stroke-linecap="round" stroke-miterlimit="10" d="M1 3l4 4 4-4"></path></svg><div class="pl-2 text-left">Balancing Acts: Equations</div></button><div class="ml-1 pl-4 collapse"><p><span>This lesson will teach you how to balance equations with formulas, such as those used to calculate interest, distance, and temperature. You will also learn how to translate these types of verbal equations into numerical ones. So, this is a chance to hone your mathematic reading skills, too.</span></p></div><button aria-pressed="false" type="button" class="px-0 text-decoration-none text-primary btn btn-link">View All Sections</button><div class="collapse"><button aria-expanded="false" type="button" class="collapsed d-flex font-weight-bold px-0 text-decoration-none text-primary btn btn-link"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 10 10" class="collapse-flip size-1 text-muted mt-1"><path fill="none" stroke="currentColor" stroke-linecap="round" stroke-miterlimit="10" d="M1 3l4 4 4-4"></path></svg><div class="pl-2 text-left">Investments, Mixtures, and Percentage Changes</div></button><div class="ml-1 pl-4 collapse"><p><span>In this lesson, you will calculate problems involving percentages, such as how much to invest at different interest rates to obtain optimum interest, and you will learn how to determine a specific quantity of a component of a mixture or solution given specific concentrations.</span></p></div><button aria-expanded="false" type="button" class="collapsed d-flex font-weight-bold px-0 text-decoration-none text-primary btn btn-link"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 10 10" class="collapse-flip size-1 text-muted mt-1"><path fill="none" stroke="currentColor" stroke-linecap="round" stroke-miterlimit="10" d="M1 3l4 4 4-4"></path></svg><div class="pl-2 text-left">Equate It in Words</div></button><div class="ml-1 pl-4 collapse"><p><span>The more you practice, the better you will be able to speak the language: the math language. Practice makes perfect! So, in this lesson, you will calculate populations, averages, lengths, and widths. You will also learn how to calculate consecutive integers, including consecutive odd and even integers.</span></p></div><button aria-expanded="false" type="button" class="collapsed d-flex font-weight-bold px-0 text-decoration-none text-primary btn btn-link"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 10 10" class="collapse-flip size-1 text-muted mt-1"><path fill="none" stroke="currentColor" stroke-linecap="round" stroke-miterlimit="10" d="M1 3l4 4 4-4"></path></svg><div class="pl-2 text-left">Proportions and Variations</div></button><div class="ml-1 pl-4 collapse"><p><span>In this lesson, you will learn ratios and how to apply them to probability and odds. You will also find out how quantities vary in equations, whether directly or indirectly, and how to apply these variations to scientific laws and equations involving weight, area, and equations of lines.</span></p></div><button aria-expanded="false" type="button" class="collapsed d-flex font-weight-bold px-0 text-decoration-none text-primary btn btn-link"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 10 10" class="collapse-flip size-1 text-muted mt-1"><path fill="none" stroke="currentColor" stroke-linecap="round" stroke-miterlimit="10" d="M1 3l4 4 4-4"></path></svg><div class="pl-2 text-left">Uniform Linear Motion</div></button><div class="ml-1 pl-4 collapse"><p><span>This lesson brings you outdoor to solve equations of uniform linear motion, with activities such as jogging, boating, and traveling. You will learn how to calculate distance, rate (speed), and time while going in the same direction, opposite directions, and with wind and water current.</span></p></div><button aria-expanded="false" type="button" class="collapsed d-flex font-weight-bold px-0 text-decoration-none text-primary btn btn-link"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 10 10" class="collapse-flip size-1 text-muted mt-1"><path fill="none" stroke="currentColor" stroke-linecap="round" stroke-miterlimit="10" d="M1 3l4 4 4-4"></path></svg><div class="pl-2 text-left">Solving Rational Equations</div></button><div class="ml-1 pl-4 collapse"><p><span>This lesson focuses on using the formula that employs the same concept as the uniform linear motion equation. You will learn to calculate how long it takes to finish a job, how much of the job is done, and at what rate the job is done, depending on the number of people doing the job.</span></p></div><button aria-expanded="false" type="button" class="collapsed d-flex font-weight-bold px-0 text-decoration-none text-primary btn btn-link"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 10 10" class="collapse-flip size-1 text-muted mt-1"><path fill="none" stroke="currentColor" stroke-linecap="round" stroke-miterlimit="10" d="M1 3l4 4 4-4"></path></svg><div class="pl-2 text-left">Algebraic Rational Equations</div></button><div class="ml-1 pl-4 collapse"><p><span>Discover some of the natural laws that govern the universe and delve into other physics concepts such as resistance, conductance, focal length, and forces while you learn some history of D-Day.</span></p></div><button aria-expanded="false" type="button" class="collapsed d-flex font-weight-bold px-0 text-decoration-none text-primary btn btn-link"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 10 10" class="collapse-flip size-1 text-muted mt-1"><path fill="none" stroke="currentColor" stroke-linecap="round" stroke-miterlimit="10" d="M1 3l4 4 4-4"></path></svg><div class="pl-2 text-left">Potpourri of Algebraic Equations</div></button><div class="ml-1 pl-4 collapse"><p><span>Potpourri, anyone? Test various problem-solving skills while you meet General Sherman and experience the gloominess of the Great Depression.</span></p></div></div></div></div><div class="py-5" data-dom-id="instructors"><div class="container"><div class="border-bottom border-dark mb-4 pb-3"><h2 class="font-weight-light sticky-nav-target" id="instructors">Instructors &amp; Support</h2></div><div><p><strong>Barbara Rolston</strong></p> <p>Barbara Rolston holds a master's degree. Since 1975, she has been taught GED preparatory classes in a variety of settings, including adult schools, community colleges, and large corporations. She also was responsible for administering the GED exam in a correctional facility for two years. Math experience includes tutoring community college students on a wide range of math topics and serving as a math consultant for a nationwide adult student assessment system.</p><p><strong>Instructor Interaction:</strong> The instructor looks forward to interacting with learners in the online moderated discussion area to share their expertise and answer any questions you may have on the course content.</p></div></div></div><div class="py-5" data-dom-id="requirements"><div class="container"><div class="border-bottom border-dark mb-4 pb-3"><h2 class="font-weight-light sticky-nav-target" id="requirements">Requirements</h2></div><div><p><strong>Prerequisites:</strong></p> <p>There are no prerequisites to take this course.</p> <p><strong>Requirements:</strong></p> <p>Hardware Requirements:</p> <ul> <li>This course can be taken on either a PC, Mac, or Chromebook.</li> </ul> <p>Software Requirements:</p> <ul> <li>PC: Windows 8 or later.</li> <li>Mac: macOS 10.6 or later.</li> <li>Browser: The latest version of Google Chrome or Mozilla Firefox are preferred. Microsoft Edge and Safari are also compatible.</li> <li><a href="https://get.adobe.com/reader/" target="_blank">Adobe Acrobat Reader</a>.</li> <li>Software must be installed and fully operational before the course begins.</li> </ul> <p>Other:</p> <ul> <li>Email capabilities and access to a personal email account.</li> </ul> <p><strong>Instructional Material Requirements:</strong></p> <p>The instructional materials required for this course are included in enrollment and will be available online.</p></div></div></div><div class="bg-light expandable-section py-5" data-dom-id="faq"><div class="container"><div class="border-bottom border-dark mb-4 pb-3"><h2 class="font-weight-light sticky-nav-target" id="faq">FAQ</h2></div><button aria-expanded="false" type="button" class="px-0 text-decoration-none text-primary btn btn-link">Expand All</button><button aria-expanded="false" type="button" class="collapsed d-flex font-weight-bold px-0 text-decoration-none text-primary btn btn-link"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 10 10" class="collapse-flip size-1 text-muted mt-1"><path fill="none" stroke="currentColor" stroke-linecap="round" stroke-miterlimit="10" d="M1 3l4 4 4-4"></path></svg><div class="pl-2 text-left"><p><strong>When can I get started?</strong></p></div></button><div class="ml-1 pl-4 collapse"><p style="margin-bottom: 10px">Instructor-Moderated: A new session of each course begins each month. Please refer&nbsp;to the session start dates for scheduling.​<br><br>Self-Guided: Your course begins immediately after you enroll.​</p></div><button aria-expanded="false" type="button" class="collapsed d-flex font-weight-bold px-0 text-decoration-none text-primary btn btn-link"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 10 10" class="collapse-flip size-1 text-muted mt-1"><path fill="none" stroke="currentColor" stroke-linecap="round" stroke-miterlimit="10" d="M1 3l4 4 4-4"></path></svg><div class="pl-2 text-left"><p><strong>How does it work?</strong></p></div></button><div class="ml-1 pl-4 collapse"><p style="margin-bottom: 10px">Instructor-Moderated: Once a course session starts, two lessons will be released each&nbsp;week for the&nbsp;6 week&nbsp;duration of your course. You will have access to all&nbsp;previously released lessons until the course ends.&nbsp;You will interact with the&nbsp;instructor through the online discussion area. There are no live sessions or&nbsp;online meetings with the instructor.<br><br>Self-Guided: You have 3 months of access to the course. After enrolling, you can learn and complete the course at your own pace, within the allotted access period. You will have the opportunity to interact with other students in the online discussion area.</p></div><button aria-expanded="false" type="button" class="collapsed d-flex font-weight-bold px-0 text-decoration-none text-primary btn btn-link"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 10 10" class="collapse-flip size-1 text-muted mt-1"><path fill="none" stroke="currentColor" stroke-linecap="round" stroke-miterlimit="10" d="M1 3l4 4 4-4"></path></svg><div class="pl-2 text-left"><p><strong>How long do I have to complete each lesson?</strong></p></div></button><div class="ml-1 pl-4 collapse"><p style="margin-bottom: 10px">Instructor-Moderated: The interactive discussion area for each lesson automatically&nbsp;closes two weeks after each lesson is released, so you're encouraged to&nbsp;complete each lesson within two weeks of its release.&nbsp;However, you will have&nbsp;access to all lessons from the time they are released until the course ends.​<br><br>Self-Guided: There is no time limit to complete each lesson, other than completing all lessons within the allotted access period. Discussion areas for&nbsp;each lesson are open for the entire duration of the course.</p></div><button aria-expanded="false" type="button" class="collapsed d-flex font-weight-bold px-0 text-decoration-none text-primary btn btn-link"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 10 10" class="collapse-flip size-1 text-muted mt-1"><path fill="none" stroke="currentColor" stroke-linecap="round" stroke-miterlimit="10" d="M1 3l4 4 4-4"></path></svg><div class="pl-2 text-left"><p><strong>What if I need an extension?</strong></p></div></button><div class="ml-1 pl-4 collapse"><p style="margin-bottom: 10px">Instructor-Moderated: Students enrolled in a six-week online class benefit from a one-time, 10-day extension for each course. No further extensions can be provided beyond these 10 days.​<br><br>Self-Guided: Because this course is self-guided, no extensions will be granted after the start of your enrollment.</p></div></div></div><div class="py-5" data-dom-id="testimonial"><div class="container"><div class="border-bottom border-dark mb-4 pb-3"><h2 class="font-weight-light sticky-nav-target" id="testimonial">Reviews</h2></div><div id="reviewsCarouselMobile" data-testid="reviews-carousel-mobile" class="mt-4 pb-5 d-md-none carousel slide"><ol class="carousel-indicators"><li class="active"></li><li></li><li></li><li></li><li></li><li></li><li></li><li></li><li></li><li></li></ol><div class="carousel-inner"><div class="active carousel-item"><div class="row"><div class="col"><div class="e2g-reviews_icon reviews-icon-small"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 100 100" class="text-white"><path d="M31.5 21.8c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5zm35.4 0c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5z" fill="currentColor"></path></svg></div><p class="font-italic mx-5 px-5">Thank you for teaching this class and taking the time to help as needed. I feel a little more confident in helping my daughter with her math homework now. I just got a job with Princeton Review to tutor students on the SAT. Taking this class refreshed my mind enough that I passed the math pre-test in order to get the job.</p></div></div></div><div class="carousel-item"><div class="row"><div class="col"><div class="e2g-reviews_icon reviews-icon-small"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 100 100" class="text-white"><path d="M31.5 21.8c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5zm35.4 0c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5z" fill="currentColor"></path></svg></div><p class="font-italic mx-5 px-5">This was a great course, taught by a knowledgeable instructor. I liked how the subject was put into a context that related to everyday life and was mixed with other subjects to make it more interesting. Thank you for making Algebra as painless as possible!</p></div></div></div><div class="carousel-item"><div class="row"><div class="col"><div class="e2g-reviews_icon reviews-icon-small"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 100 100" class="text-white"><path d="M31.5 21.8c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5zm35.4 0c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5z" fill="currentColor"></path></svg></div><p class="font-italic mx-5 px-5">This course was informative and very useful to me in my future educational endeavors. I loved the instructor's sense of humor and teaching style, she made algebra practical and understandable and took the "fear" out of it.</p></div></div></div><div class="carousel-item"><div class="row"><div class="col"><div class="e2g-reviews_icon reviews-icon-small"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 100 100" class="text-white"><path d="M31.5 21.8c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5zm35.4 0c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5z" fill="currentColor"></path></svg></div><p class="font-italic mx-5 px-5">Thank you for this course. It really was what I was looking for; the format, the time flexibility, and the easy accessibility made all the positive difference for me. Thank you very much!</p></div></div></div><div class="carousel-item"><div class="row"><div class="col"><div class="e2g-reviews_icon reviews-icon-small"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 100 100" class="text-white"><path d="M31.5 21.8c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5zm35.4 0c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5z" fill="currentColor"></path></svg></div><p class="font-italic mx-5 px-5">The class is an algebraic workout doing various problems and review of previous algebra class work. I recommend this course to those who are weak in Algebra.</p></div></div></div><div class="carousel-item"><div class="row"><div class="col"><div class="e2g-reviews_icon reviews-icon-small"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 100 100" class="text-white"><path d="M31.5 21.8c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5zm35.4 0c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5z" fill="currentColor"></path></svg></div><p class="font-italic mx-5 px-5">I really enjoyed this course and I am satisfied with the material covered. Everything was straightforward with good examples. I will recommend this course to friends.</p></div></div></div><div class="carousel-item"><div class="row"><div class="col"><div class="e2g-reviews_icon reviews-icon-small"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 100 100" class="text-white"><path d="M31.5 21.8c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5zm35.4 0c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5z" fill="currentColor"></path></svg></div><p class="font-italic mx-5 px-5">This course really helped me to rethink and improve on skills that I have not used in over 20 years. I took this course a refresher so I can re-test for my math placement. I'm hoping that this course will do that. This course was also very affordable and interesting. At the very least it has taught me some very good core algebra functions and applied them to my life.</p></div></div></div><div class="carousel-item"><div class="row"><div class="col"><div class="e2g-reviews_icon reviews-icon-small"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 100 100" class="text-white"><path d="M31.5 21.8c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5zm35.4 0c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5z" fill="currentColor"></path></svg></div><p class="font-italic mx-5 px-5">Thank you for teaching me this course! I developed new skills as I hoped. Your lessons were very detailed and helped me understand the subject easily.</p></div></div></div><div class="carousel-item"><div class="row"><div class="col"><div class="e2g-reviews_icon reviews-icon-small"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 100 100" class="text-white"><path d="M31.5 21.8c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5zm35.4 0c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5z" fill="currentColor"></path></svg></div><p class="font-italic mx-5 px-5">I would just like to say that I have thoroughly enjoyed taking this course. I have to admit I was a little confounded by some of the problems in the course, but those were the ones that challenged me to think harder.</p></div></div></div><div class="carousel-item"><div class="row"><div class="col"><div class="e2g-reviews_icon reviews-icon-small"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 100 100" class="text-white"><path d="M31.5 21.8c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5zm35.4 0c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5z" fill="currentColor"></path></svg></div><p class="font-italic mx-5 px-5">Thank you Sharon for the opportunity to learn this material with you. It exceeded by expectations, since there was a lot I had forgotten since high school. I really appreciated the real-life examples, and how you were able to explain the mathematical concepts easily.</p></div></div></div></div></div><div id="reviewsCarousel" data-testid="reviews-carousel" class="mt-4 pb-5 d-none d-md-block carousel slide"><ol class="carousel-indicators"><li class="active"></li><li></li><li></li><li></li><li></li></ol><div class="carousel-inner"><div class="active carousel-item"><div class="mx-0 row"><div class="col"><div class="e2g-reviews_icon reviews-icon-large"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 100 100" class="text-white"><path d="M31.5 21.8c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5zm35.4 0c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5z" fill="currentColor"></path></svg></div><p class="font-italic mx-5 px-5">Thank you for teaching this class and taking the time to help as needed. I feel a little more confident in helping my daughter with her math homework now. I just got a job with Princeton Review to tutor students on the SAT. Taking this class refreshed my mind enough that I passed the math pre-test in order to get the job.</p></div><div class="col"><div class="e2g-reviews_icon reviews-icon-large"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 100 100" class="text-white"><path d="M31.5 21.8c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5zm35.4 0c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5z" fill="currentColor"></path></svg></div><p class="font-italic mx-5 px-5">This was a great course, taught by a knowledgeable instructor. I liked how the subject was put into a context that related to everyday life and was mixed with other subjects to make it more interesting. Thank you for making Algebra as painless as possible!</p></div></div></div><div class="carousel-item"><div class="mx-0 row"><div class="col"><div class="e2g-reviews_icon reviews-icon-large"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 100 100" class="text-white"><path d="M31.5 21.8c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5zm35.4 0c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5z" fill="currentColor"></path></svg></div><p class="font-italic mx-5 px-5">This course was informative and very useful to me in my future educational endeavors. I loved the instructor's sense of humor and teaching style, she made algebra practical and understandable and took the "fear" out of it.</p></div><div class="col"><div class="e2g-reviews_icon reviews-icon-large"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 100 100" class="text-white"><path d="M31.5 21.8c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5zm35.4 0c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5z" fill="currentColor"></path></svg></div><p class="font-italic mx-5 px-5">Thank you for this course. It really was what I was looking for; the format, the time flexibility, and the easy accessibility made all the positive difference for me. Thank you very much!</p></div></div></div><div class="carousel-item"><div class="mx-0 row"><div class="col"><div class="e2g-reviews_icon reviews-icon-large"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 100 100" class="text-white"><path d="M31.5 21.8c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5zm35.4 0c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5z" fill="currentColor"></path></svg></div><p class="font-italic mx-5 px-5">The class is an algebraic workout doing various problems and review of previous algebra class work. I recommend this course to those who are weak in Algebra.</p></div><div class="col"><div class="e2g-reviews_icon reviews-icon-large"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 100 100" class="text-white"><path d="M31.5 21.8c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5zm35.4 0c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5z" fill="currentColor"></path></svg></div><p class="font-italic mx-5 px-5">I really enjoyed this course and I am satisfied with the material covered. Everything was straightforward with good examples. I will recommend this course to friends.</p></div></div></div><div class="carousel-item"><div class="mx-0 row"><div class="col"><div class="e2g-reviews_icon reviews-icon-large"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 100 100" class="text-white"><path d="M31.5 21.8c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5zm35.4 0c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5z" fill="currentColor"></path></svg></div><p class="font-italic mx-5 px-5">This course really helped me to rethink and improve on skills that I have not used in over 20 years. I took this course a refresher so I can re-test for my math placement. I'm hoping that this course will do that. This course was also very affordable and interesting. At the very least it has taught me some very good core algebra functions and applied them to my life.</p></div><div class="col"><div class="e2g-reviews_icon reviews-icon-large"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 100 100" class="text-white"><path d="M31.5 21.8c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5zm35.4 0c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5z" fill="currentColor"></path></svg></div><p class="font-italic mx-5 px-5">Thank you for teaching me this course! I developed new skills as I hoped. Your lessons were very detailed and helped me understand the subject easily.</p></div></div></div><div class="carousel-item"><div class="mx-0 row"><div class="col"><div class="e2g-reviews_icon reviews-icon-large"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 100 100" class="text-white"><path d="M31.5 21.8c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5zm35.4 0c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5z" fill="currentColor"></path></svg></div><p class="font-italic mx-5 px-5">I would just like to say that I have thoroughly enjoyed taking this course. I have to admit I was a little confounded by some of the problems in the course, but those were the ones that challenged me to think harder.</p></div><div class="col"><div class="e2g-reviews_icon reviews-icon-large"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 100 100" class="text-white"><path d="M31.5 21.8c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5zm35.4 0c-6.8 0-12.3 5.7-12.3 12.6 0 7 5.5 12.6 12.3 12.6 12.3 0 4.1 24.4-12.3 24.4v5.9c29.3.2 40.7-55.5 12.3-55.5z" fill="currentColor"></path></svg></div><p class="font-italic mx-5 px-5">Thank you Sharon for the opportunity to learn this material with you. It exceeded by expectations, since there was a lot I had forgotten since high school. I really appreciated the real-life examples, and how you were able to explain the mathematical concepts easily.</p></div></div></div></div><a class="carousel-control-next" role="button" href="#"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 10 10" aria-hidden="true" class="arrow-next text-dark"><path fill="none" stroke="currentColor" stroke-linecap="round" stroke-miterlimit="10" d="M1 3l4 4 4-4"></path></svg><span class="sr-only">Next</span></a></div></div></div><div class="related-products py-5" data-dom-id="relatedCourses"><div class="container"><div class="border-bottom border-dark mb-4 pb-3"><h2 class="font-weight-light sticky-nav-target" id="relatedCourses">Related Courses</h2></div><div class="d-md-none"><a aria-label="Math Refresher" href="/courses/math-and-science/mathematics-and-science/ilc/everyday-math" data-testid="related-product-link-/courses/math-and-science/mathematics-and-science/ilc/everyday-math" class="d-block pl-0 mt-3 text-reset text-decoration-none btn 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Discussion areas for\u0026nbsp;each lesson are open for the entire duration of the course.\u003c/p\u003e"},{"header":"\u003cp\u003e\u003cstrong\u003eWhat if I need an extension?\u003c/strong\u003e\u003c/p\u003e","content":"\u003cp style=\u0022margin-bottom: 10px\u0022\u003eInstructor-Moderated: Students enrolled in a six-week online class benefit from a one-time, 10-day extension for each course. No further extensions can be provided beyond these 10 days.​\u003cbr\u003e\u003cbr\u003eSelf-Guided: Because this course is self-guided, no extensions will be granted after the start of your enrollment.\u003c/p\u003e"}],"title":"FAQ"},"reviews":{"domId":"testimonial","title":"Reviews","reviews":["Thank you for teaching this class and taking the time to help as needed. I feel a little more confident in helping my daughter with her math homework now. I just got a job with Princeton Review to tutor students on the SAT. Taking this class refreshed my mind enough that I passed the math pre-test in order to get the job.","This was a great course, taught by a knowledgeable instructor. I liked how the subject was put into a context that related to everyday life and was mixed with other subjects to make it more interesting. Thank you for making Algebra as painless as possible!","This course was informative and very useful to me in my future educational endeavors. I loved the instructor\u0027s sense of humor and teaching style, she made algebra practical and understandable and took the \u0022fear\u0022 out of it.","Thank you for this course. It really was what I was looking for; the format, the time flexibility, and the easy accessibility made all the positive difference for me. Thank you very much!","The class is an algebraic workout doing various problems and review of previous algebra class work. I recommend this course to those who are weak in Algebra.","I really enjoyed this course and I am satisfied with the material covered. Everything was straightforward with good examples. I will recommend this course to friends.","This course really helped me to rethink and improve on skills that I have not used in over 20 years. I took this course a refresher so I can re-test for my math placement. I\u0027m hoping that this course will do that. This course was also very affordable and interesting. At the very least it has taught me some very good core algebra functions and applied them to my life.","Thank you for teaching me this course! I developed new skills as I hoped. Your lessons were very detailed and helped me understand the subject easily.","I would just like to say that I have thoroughly enjoyed taking this course. I have to admit I was a little confounded by some of the problems in the course, but those were the ones that challenged me to think harder.","Thank you Sharon for the opportunity to learn this material with you. It exceeded by expectations, since there was a lot I had forgotten since high school. 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