How do u rewrite an absolute value inequality as a compound inequality?

Question

Heres the problem: Ix+8I < 5

Answer 1

You write 2 inequalities, once for each possible situation:
where | x + 8 | = x + 8 (for x >= -8)
and | x + 8 | = - ( x + 8 ) = - x - 8 (for x < -8)

x + 8 < 5
x < - 3

- x - 8 < 5
- x < 13
x > -13 (remember to change inequality when multiplying by -1)


The solution is the combination of these inequalities...

-13 < x < -3

Answer 2

x+8<5
and
x+8>-5

Answer 3

lol i'm learning the same thing(good thing i'm azn i know math) just make -5