Algebra II Workbook - Wayne County Public Schools

LESSON
1.7
NAME _________________________________________________________ DATE ____________
Practice with Examples
For use with pages 50–56
GOAL
Solve absolute value equations and inequalities and use absolute value
equations and inequalities to solve real-life problems
EXAMPLE 1
EXAMPLE 2
VOCABULARY
The absolute value of a number x, written is the distance the
number is from 0 on a number line. The absolute value of a number is
always nonnegative.
Solving an Absolute Value Equation
Solve
SOLUTION
1 2x 5
1
7
Write original equation.
1
2 x 5 7 or 2 x 5 7 Expression can be 7 or 7.
1
2 x 2 or
2 x 12 Subtract 5 from each side.
x 4 or
1x 24
The solutions are 4 and 24.
When x 4:
When x 24:
Exercises for Example 1
Solve the equation.
Multiply each side by
1. 2. 3.
Solving an Inequality of the Form
Solve
1 2x 5 7.
r 8 2 1 224 5 7 7
2x 3 < 7. ax b < c 8 3n 16
SOLUTION
2x 3 < 7.
7 < 2x 3 < 7
10 < 2x < 4
1
5 < x < 2
24 5 7 7
x ,
2m 5 9
Write original inequality.
Write equivalent compound inequality.
Subtract 3 from each expression.
Divide each expression by 2.
The solutions are all real numbers greater than 5 and less than 2.
2
1 .
Chapter 1
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Algebra 2 19
Practice Workbook with Examples