Which of the following is a solution for the absolute value inequality |2x – 3| > 6?

This breaks into two inequalities:

2x - 3 > 6

and

-2x + 3 > 6



2x - 3 > 6

Add 3 to both sides:

2x > 9

Divide 2 to both sides:

x > 4.5



-2x + 3 > 6

Subtract 3 to both sides:

-2x > 3

Divide -2 to both sides:

x < -1.5

|2x-3|>6
2x-3>6    and   2x-3<-6
for 2x-3>6
add 3
2x>9
divide by 2
x>9/2
for 2x-3<-6
add 3
2x<-3
divide by 2
x<-3/2
those are your two answers