### Home > AC > Chapter 10 > Lesson 10.2.1 > Problem10-52

10-52.

Use the results from problem 10-51 to help you find all possible values for x in each of the following equations.

1. $| x | = 4$

The absolute values of what two numbers equals $4$?

$x=-4$ or $4$

1. $| x | = 100$

Follow the steps of part (a).

1. $|x|=-3$

Can the absolute value of any number be negative?

1. $|x-2|=5$

The absolute values of $-5$ and $5$ equal $5$.

$x-2=5$ or $x-2=-5$
Now solve both equations for $x$.

$x=7$ or $-3$