SOLUTION: What is the solution for the compound inequality 3x + 8 < 2 or x + 12 > 2

Click here to see ALL problems on Inequalities

Question 549347: What is the solution for the compound inequality 3x + 8 < 2 or x + 12 > 2 - x ?

Found 2 solutions by mathie123, karaoz:
Answer by mathie123(224) (Show Source):
You can put this solution on YOUR website!
(1)
(2)
Looking at (1) we can see that:

Looking at (2) we can see that

So to satisfy both (1) and (2) we must have

Answer by karaoz(32) (Show Source):
You can put this solution on YOUR website!
Given:
(1) 3x + 8 < 2
(2) x + 12 > 2 - x

Simplify both inequalities:
take away 8 from both sides of (1) and add x-12 to both sides of (2).
(1) 3x < -6
(2) 2x > -10

Simplify further:
divide (1) by 3 and divide (2) by 2
(1) x < -2
(2) x > -5

Assuming compound inequality means that both inequalities have to be satisfied at the same time then the last set of two inequalities represent solution to the problem. This solution can be also expressed in the following form:
-5 < x < -2.

Translated into English, the solution is:
x has to be larger than -5 and smaller than -2.

SOLUTION: What is the solution for the compound inequality 3x + 8 < 2 or x + 12 > 2 - x ?