1.7

1
1.7 Solve Absolute Value Equations and
Inequalities

• Recall that the absolute value of a number x,
  written x, is the distance the number is from 0
  on a number line. This understanding of absolute
  value can be extended to apply to simple absolute
  value equations.

2
1.7 Solve Absolute Value Equations and
Inequalities
3
1.7 Solve Absolute Value Equations and
Inequalities

• Example 1
• Solve x 7 7

4
1.7 Solve Absolute Value Equations and
Inequalities

• Example 1b
• Solve 2x 9 15

5
1.7 Solve Absolute Value Equations and
Inequalities
6
1.7 Solve Absolute Value Equations and
Inequalities

• Example 2
• Solve 5x 10 45

7
1.7 Solve Absolute Value Equations and
Inequalities

• Example 2
• Solve 4x 10 28

8
1.7 Solve Absolute Value Equations and
Inequalities

• Extraneous Solutions
• When you solve an absolute value equation, it is
  possible for a solution to be extraneous. An
  extraneous solution is an apparent solution that
  must be rejected because it does not satisfy the
  original equation.

9
1.7 Solve Absolute Value Equations and
Inequalities

• Example 3
• Solve 2x 12 4x

10
1.7 Solve Absolute Value Equations and
Inequalities

• Example 3b
• Solve 4x 10 6x 4

11
1.7 Solve Absolute Value Equations and
Inequalities
12
1.7 Solve Absolute Value Equations and
Inequalities

• Example 4
• Solve 4x 5 gt 13

13
1.7 Solve Absolute Value Equations and
Inequalities

• Example 4b
• Solve 3x 7 gt 5