Algebraic Proofs: Format & Examples

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  • 0:01 An Algebraic Proof
  • 0:38 Format
  • 1:22 Example 1
  • 2:17 Example 2
  • 3:02 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Algebraic proofs are actually kind of cool. Watch this video lesson to see how an algebraic proof shows you the mathematical reasoning behind your algebraic solutions. Use this method to show your teachers why your answer is the right one.

An Algebraic Proof

An algebraic proof shows the logical arguments behind an algebraic solution. It explains the reasoning behind each step. This is something you need to know when it comes to taking standardized tests, and this is also a good way to prove to your teacher or other people that your answer is the correct one (that is, if you did it correctly to begin with). And if you didn't, this way may actually help you troubleshoot and find where you made your mistake. Algebraic proofs look something like this:

algebraic proof

You see your problem at the top and then you can see each of the steps you take to solve your problem.


All algebraic proofs follow the same format. They begin with the problem and sometimes its solution. Your job is to prove that the solution is right. You use a two-column table format to write down your steps and the mathematical reasons for your steps. Your steps go in the left column and your reasons in the right column. Your mathematical reasons have to be a proven mathematical concept or rule, such as the subtraction property of equality and other such rules. Whatever is stated or given to you in the problem has the mathematical reason of 'given.' If you are simply asked to solve an algebraic problem, you can use the algebraic proofs format to prove your answers are correct.

Let's take a look at a couple of examples now.

Example 1

Given 4x - 10 = 7 - 2x, prove that x = 17 / 6

Looking at this algebraic problem, you know exactly how to go about finding the solution. You go through your steps and you write each step down line by line in the left column. In the right column, you write the mathematical reason or rule that you used for each step. To solve for your variable, you first add the 2x to both sides by using the addition property of equality. Then you add the 10 to both sides by using the addition property of equality again. Then, you divide by the 6 on both sides by using the division property of equality. Your algebraic proof looks like this:

algebraic proof

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