Question

Solve and graph the absolute value inequality: |2x + 4| > 8

Answer 1

This absolute value inequality has two answers: one for -x<y and another for x>y. So, the first thing to do is clear the absolute value bars by splitting the inequality into two. Then I'll solve the two linear inequalities.

\[|2x+4|>8 \rightarrow \]

| 2x+4 | > 8

Then 2x>4, so x>2. This is the solution for the positive x.

Then, we transform it to a negative inequality multiplying it by -1:

2x-4<-8

2x<-4

x<-2 This is the solution for the negative x.