Solve the absolute value inequality

Question

Solve the absolute value inequality:

5|x+3|-2<18

Answer 1

5|x + 3| - 2 < 18

5|x + 3| < 20

|x + 3| < 4

Now, remembering that absolute value is the distance from 0 and 4 and -4 are equidistant from 0, x + 3 has to be less than 4 or greater than -4, since 3 and -3 are also equidistant from 0 and therefore have the same absolute value.

x + 3 < 4

x < 1

x + 3 > -4

x > -7

Since those both fall in the same area of the number line...

-7 < x < 1, AKA x > -7 and x < 1