Algebra 2: How to write a proper explanation

Explain to someone who doesn’t know a lot about math why you can never find an x which would make the following

statement true:

SOME SOLUTIONS FROM THE CLASS 1

1. You can never find an x that would make that statement because no matter what, the absolute value would still equal a negative number. This is not possible because an absolute value is a distance away from 0 and a number cannot be a negative distance away from 0.

2. Once you solve it and have the absolute value alone, it equals -1. An absolute value can never equal a negative number.

3. You can never find x because the answer is negative and an absolute value problem with a negative after the equal sign is not possible.

4. Because that would make the absolute value of which is not possible because absolute value is the distance from 0 to a number on the number line. Therefore it can not be a negative.

5. An absolute value can never be equal to a negative number.6. The other side of the equation is negative, leaving no possible solution to the problem.7. An absolute value is the distance a number is from 0 and having a (-) distance is impossible so there cannot be a

negative absolute value product/sum/quotient/etc…8. There can be no solution because when solving for x, there can never be a negative distance from zero, which is

the absolute value. For example, there is no such thing as negative inches. 9. Because when absolute value is equal to a negative number there is no solution, and that’s because there isn’t a

way something can move a negative distance, and absolute value is distance on a # line.

General problems with these explanations:

If the question asked

“Explain why the solution to has no solution”

A good solution would read:1 Almost no one in the class got full credit for this problem. But that was expected because I haven’t “taught” you to write good explanations yet. (That is the reason why I made question 27 “extra credit.” Surprisingly, most all of you wrote really cogent and wonderful explanations for that problem.) The 9 solutions that I picked to share were totally random.

Let’s consider what the absolute value function does. It “strips” the number inside of the absolute value symbols of its negative sign. For example , while . Geometrically, the absolute value of a number represents the

distance that number is away from the origin on the number line. Hence the value of must be zero or positive.

So for a problem to ask when , it is essentially asking us when is negative, because anything less

than -2 is negative. Since we know that must be zero or positive, we know that there is no way that could ever be negative. Hence no value of could ever satisfy the inequality.

What are the qualities that make this a good solution?

Is there a way to improve the solution?

If I were to write a proper solution to the question 26 from the assessment, I would now say: