Solving absolute value inequality - Solve for z. 2 3. Use integers, proper fractions, or improper fractions in simplest form.

Sangeetha Pulapaka (last edited 4 years ago) (Expert, Educator @Qalaxia)

STEP 1: Recal how to solve for an an inequality

STEP 2: Recall what are compound inequalities

STEP 3: Solve for z

2 <|z+2|< 4

can be written as 2< |z+2| and |z+2|> 4

Solving 2<|z+2|

2 -2 < z+ 2 - 2

0 < z. This can be written as z>0

Next soving |z+2|>4

z+2-2 > 4 - 2

z > 2

Combining both can be written as 0< z <2

Skills to recall:

What are absolute values

What are absolute functions

What are absolute equations