# What is the solution set for #absx - 1 < 4#?

##### 1 Answer

#### Explanation:

To solve this absolute value inequality, first isolate the modulus on one side by adding

#|x| - color(red)(cancel(color(black)(1))) + color(red)(cancel(color(black)(1))) < 4 + 1#

#|x| < 5#

Now, depending on the possible sign of

#x>0 implies |x| = x#

This means that the inequality becomes

#x < 5#

#x<0 implies |x| = -x#

This time, you have

#-x < 5 implies x> -5#

These two conditions will determine the solution set for the absolute value inequality. Since the inequality holds true for **smaller** than that will be excluded.

LIkewise, since **greater** than