solve for |2x-7|>11

Question

I would like to solve the absolute value inequality equation.

Answer 1

The inequality is |2x -7|>11.

The absolute value inequality |2x -7|>11 is equivalent to 2x -7 > 11 or 2x -7 < -11.

Solve the inequality 1: 2x -7 > 11.

Add 7 to each side.

2x -7 +7 > 11+7

2x > 18

Divide each side by 2.

2x/2 >18/2

Cancel common terms.

x >9.

Solve the inequality 2:2x -7 < -11.

Add 7 to each side.

2x -7+7 < -11+7

2x < -4

Divide each side by 2.

2x/2 < -4/2

Cancel common terms.

x < -2.

The solution set is { x|x >9 or x < -2 }.