# How do you solve the inequality: #abs(x - 8) < 5#?

##### 1 Answer

Aug 14, 2015

#### Explanation:

In order to solve this absolute value inequality, you need totake into account the two possible signs the expression inside the modulus can have

#x-8>0 implies |x-8| = x - 8#

The inequality will become

#x - 8 < 5#

#x < 13#

#x - 8 < 0 implies |x - 8| = -(x-8)#

This time, the inequality will be

#-(x-8) < 5#

#-x + 8 < 5#

#x > 3#

So, the solution set for this inequality will include any value of *bigger* than *smaller* than

This means that you have