# What is the solution to the inequality absx≤7?

Sep 1, 2015

$\left[- 7 , 7\right]$

#### Explanation:

There are two possibilities:

Either x is greater than 0, in which case $x \le 7$

Or, x is less than 0, in which case $x \ge - 7$ (because in order for the absolute value of x to be less than 7, x must be greater than -7.)

So, x has to be less than or equal to 7, and x has to be greater than -7. So, the solution set will be "from -7 to 7, inclusive". This can be written like this:

$\left[- 7 , 7\right]$