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Pre-Algebra: Writing, Solving Multi-Step Equations

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About this Lesson

  • Type: Video Tutorial
  • Length: 1:57
  • Media: Video/mp4
  • Posted: 01/28/2009
  • Use: Watch Online & Download
  • Download: MP4 (iPod compatible)
  • Size: 28 MB

This lesson is part of the series: Pre-Algebra Review

A multi-step equation is an equation that calls for more than two operations to be performed. It will require forethought to solve and careful consideration of the order of operations. In this lesson, Professor Burger shows you how to use properties, such as the distributive property, to simplify the equation. Then you will want to combine like terms to further simplify the equation. Once you have isolated the variable term, you can finally solve the equation.

This lesson is perfect for review for a CLEP test, mid-term, final, summer school, or personal growth!

Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

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Thinkwell
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Founded in 1997, Thinkwell has succeeded in creating "next-generation" textbooks that help students learn and teachers teach. Capitalizing on the power of new technology, Thinkwell products prepare students more effectively for their coursework than any printed textbook can. Thinkwell has assembled a group of talented industry professionals who have shaped the company into the leading provider of technology-based textbooks. For more information about Thinkwell, please visit www.thinkwell.com or visit Thinkwell's Video Lesson Store at http://thinkwell.mindbites.com/.

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WRITING AND SOLVING MULTI-STEP EQUATIONS

Let’s solve the equation. 5 times m minus 3 plus 1 equals 21. Lots of stuff going on here, this is definitely a multi-step equation. The thing to notice is that the parentheses are there. That’s a cue that we have to undo that parentheses first. That takes priority. So what we have to do is use the distributive property to take the 5 and multiply it through by the m and also multiply it through by the 3, and then subtract the 2. We’ve got to remember to distribute.

If we distribute, what do we see? What we see is 5m minus 15. You see? 5m minus 15 plus 1 equals 21. Now I can combine terms. There are no other m’s there except for the 5m, but here I have negative 15 plus 1 is negative 14, and that equals 21, and so now what can I do? Now I want to get the m’s all by themselves, I want to undo the subtracting of 14 by doing what? By adding 14 to this side, and to keep things balanced I’ll add to the other side. So everything is fair, all is fair in a balanced equation. 5m, and this 14 minus 14 is 0, and here I have 35. Then I want to undo the multiplication by 5 to get m all by itself, so I divide both sides by 5, and m equals 35 divided by 5 is 7. The answer is m equals 7.

Again, a multi-step equation just requires us to think about orders of operation and carefully go through. In this case, the parentheses take priority. I have to distribute first, and then combine the constants, then isolate the m, and then divide. Cool.

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