1. 3-6 Absolute Value Equations and Inequalities
Hubarth
Algebra

2. Solving Absolute Value Equations
*Note* an absolute value can never equal 0

3. Ex 1 Solving Absolute Value Equations
Solve and check |a| – 3 = 5.
First, get the absolute value by itself
|a| – = Add 3 to each side.
|a| = 8 Simplify.
Second set the absolute value equal to itself and its opposite
a = 8 or a = –8 Definition of absolute value.

4. Ex 2 Solving an Absolute Value Equation
Solve |3c – 6| = 9.
The absolute value is by itself, set equal to itself and its opposite
3c – 6 = c – 6 = –9
3c – = c – = –9 + 6
3c = c = –3 3c 3 = 15 –3
c = 5
c = –1
The value of c is 5 or –1.

5. Solving Absolute Value Inequalities
You solve absolute value inequalities the same as equations. The only difference is you
must also flip the inequality when solving.

6. Ex 3 Solving an Absolute Value Inequality
Solve |y – 5| Graph the solutions.
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7. Practice
-1, 1
-5, 5
6, -6
-4, 8
-2, 2
no solution
w<-7 or w>3 -7 3