Find all the values of x for which f(x) >4

Question

|2x+3| -1

Answer 1

The absolute value inequality is |2x + 3| - 1 > 4.

Add 1 to each side.

|2x + 3| > 5

|2x + 3| > 5 is equivalent to 2x + 3 > 5 or 2x + 3 < - 5.

Solve the inequality 1 : 2x + 3 > 5 for x.

Subtract 3 from each side.

2x > 2

Divide each side by 2.

x > 1.

 

Solve the inequality 2 : 2x + 3 < - 5 for x.

Subtract 3 from each side.

2x < - 8

Divide each side by 2.

x < - 4.

 

The solution set is {x | x > 1 or x < - 4}.