Question

Solve for x. |2x - 8| > 6

Answer 1

Solution is x > 7 or x < 1.

Explanation:

|2x - 8| > 6

This is equivalent to 2x - 8 > 6 or 2x - 8 < -6

2x - 8 > 6

2x > 14

x > 7.

2x - 8 < -6

2x < 2

x < 1.

Answer 2

Explanation:

`|2x-8|>6\iff 2x-8>6\ or\ 2x-8<-6\qquad\text{add 8 to both sides}\\\\2x-8+8>6+8\ or\ 2x-8+8<-6+8\\\\2x>14\ or\ 2x<2\qquad\text{divide both sides by 2}\\\\x>7\ or\ x<1 \to x\in(-\infty,\ 1)\ \cup\ (7,\ \infty)`