Solving Absolute Value Inequalities

Step 1 Isolate the absolute value.

Add 10 to both sides.

Divide both sides by 4.

Step 2 Make the substitution w = 2x - 7.

Step 3 Use the Absolute Value Principle to solve for w.

Step 4 Replace w with 2x - 7.

Step 5 Solve for x.

Add 7 to both sides.

Divide both sides by 2.

Step 6 Check the answer.

We leave the check to you.

So, the solution is x < -4 or x > 11.

4|2x - 7| > 60

|2x - 7| > 15

|w| > 15

w < -15 or w > 15

2x - 7 < -15 or 2x - 7 > 15

2x < -8 or 2x > 22

x < -4 or x > 11

 Step 1 Isolate the absolute value.

Add 12 to both sides.

Divide both sides by -5 and reverse the direction of the inequality symbol.

-5|x| < 40

|x| > -8