Free Algebra
Tutorials!
 
Home
Systems of Linear Equations and Problem Solving
Solving Quadratic Equations
Solve Absolute Value Inequalities
Solving Quadratic Equations
Solving Quadratic Inequalities
Solving Systems of Equations Row Reduction
Solving Systems of Linear Equations by Graphing
Solving Quadratic Equations
Solving Systems of Linear Equations
Solving Linear Equations - Part II
Solving Equations I
Summative Assessment of Problem-solving and Skills Outcomes
Math-Problem Solving:Long Division Face
Solving Linear Equations
Systems of Linear Equations in Two Variables
Solving a System of Linear Equations by Graphing
Ti-89 Solving Simultaneous Equations
Systems of Linear Equations in Three Variables and Matrix Operations
Solving Rational Equations
Solving Quadratic Equations by Factoring
Solving Quadratic Equations
Solving Systems of Linear Equations
Systems of Equations in Two Variables
Solving Quadratic Equations
Solving Exponential and Logarithmic Equations
Solving Systems of Linear Equations
Solving Quadratic Equations
Math Logic & Problem Solving Honors
Solving Quadratic Equations by Factoring
Solving Literal Equations and Formulas
Solving Quadratic Equations by Completing the Square
Solving Exponential and Logarithmic Equations
Solving Equations with Fractions
Solving Equations
Solving Linear Equations
Solving Linear Equations in One Variable
Solving Linear Equations
SOLVING QUADRATIC EQUATIONS USING THE QUADRATIC FORMULA
SOLVING LINEAR EQUATIONS
 
Try the Free Math Solver or Scroll down to Tutorials!

 

 

 

 

 

 

 

 
 
 
 
 
 
 
 
 

 

 

 
 
 
 
 
 
 
 
 

Please use this form if you would like
to have this math solver on your website,
free of charge.


Solve Absolute Value Inequalities

Goal • Solve absolute value inequalities.

Example 1 Solve an absolute value inequality

Solve the inequality. Graph your solution.

a. |x| ≤ 9
b. |x| > 1/4

Solution
a. The distance between x and 0 is less than or equal
to 9. So, -9 ≤ x ≤ 9 . The solutions are all real
numbers less than or equal to 9 and greater than
or equal to -9 .

b. The distance between x and 0 is greater than 1/4.
So, x > 1/4 or x < -1/4. The solutions are all real
numbers greater than 1/4
or less than -1/4.

SOLVING ABSOLUTE VALUE INEQUALITIES
• The inequality |ax + b|< c where c > 0 is equivalent
to the compound inequality -c < ax + b < c.
• The inequality |ax + b|> c where c > 0 is equivalent
to the compound inequality ax + b < -c or ax + b > c.

These statements are also true for inequalities involving
≥ and ≤.

Example 2 Solve an absolute value inequality

Solve |2x - 7|< 9. Graph your solution.

|2x - 7|< 9 Write original inequality.
-9 < 2x - 7 < 9 Rewrite as compound inequality.
-2 < 2x < 16 Add 7 to each expression.
-1 < x < 8 Divide each expression by 2 .

The solutions are all real numbers greater than -1
and less than 8 . Check several solutions in the original
inequality.

Example 3 Multiple Choice Practice

What is the solution of the inequality |x + 8| - 4 ≥ 2?

Solution

|x + 8| - 4 ≥ 2 Write original
inequality.
|x + 8|≥ 6 Add 4 to
each side.
x + 8 ≥ 6 or x + 8 ≤ -6 Rewrite as
compound
inequality.
x ≥ -2 or x ≤ -14 Subtract 8
from each side.

The correct answer is D . A B C D

• Guided Practice Solve the inequality. Graph your
solution.

SOLVING INEQUALITIES

One-Step and Multi-Step Inequalities
• Follow the steps for solving an equation, but reverse
the inequality symbol when multiplying or dividing
by a negative number .

Compound Inequalities
• If necessary, rewrite the inequality as two separate
inequalities. Then solve each inequality separately.
Include and or or in the solution.

Absolute Value Inequalities
• If necessary, isolate the absolute value expression on
one side of the inequality. Rewrite the absolute value
inequality as a compound inequality . Then solve
the compound inequality.

All Right Reserved. Copyright 2005-2017