FreeAlgebra                             Tutorials!

Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# Solving Absolute Value Inequalities

## Solving an Absolute Value Inequality of the Form | x| > a

Example 1

Solve: -10 + 4|2x - 7| > 50

 Solution 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. -10 + 4|2x - 7| > 50  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

Example 2

Solve: -5|x| - 12 < 28

 Solution 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| - 12 < 28  -5|x| < 40 |x| > -8

Since |x| represents a nonnegative number, it is greater than -8 for all values of x.

Therefore, the solution is all real numbers.

 All Right Reserved. Copyright 2005-2024