### Home > GB8I > Chapter 9 Unit 10 > Lesson INT1: 9.1.3 > Problem9-33

9-33.

Solve each equation. Be sure to find all possible solutions and check your solutions.

1. $|x| = 7$

The absolute value of $x$ is $7$, which means $x$ is $7$ away from zero. Which number or numbers are $7$ away from zero?

$7$ and $-7$

1. $| 2 x | = 32$

$2x$ is $32$ units away from zero, so x is only half as far from zero.

1. $| x + 7 | = 10$

After adding $7$ to $x$, it is only $10$ away from zero. Find the number or numbers $10$ away from zero, and subtract $7$ from them.

$3$ and $-17$

1. $5|x|=35$

Divide by $5$, then solve.

$x = ±7$