1. Linear Inequalities and Absolute Value Inequalities
Chapter 8
A Transition
Section 2
Linear Inequalities and Absolute Value Inequalities

2. Solving Linear Inequalities
Solving a linear inequality is similar to solving a linear equation, with the exception that multiplying or dividing both sides of an inequality by a negative number changes the direction of the inequality.

3. Solving Linear Inequalities
Solve

4. Solving Linear Inequalities
Solve

5. Compound Inequalities
A compound inequality is made up of two or more individual inequalities.

6. Compound Inequalities
Solve or or

7. Compound Inequalities
Solve

8. Solving Absolute Value Inequalities
For any expression X and any positive number a, the solutions to the inequality
can be found by solving the compound inequality

9. Solving Absolute Value Inequalities
Solve:

10. Solving Absolute Value Inequalities
Solve:
An absolute value cannot be less than a negative number, so the inequality has no solution.

11. Solving Absolute Value Inequalities
For any expression X and any positive number a, the solutions to the inequality
can be found by solving the compound inequality or

12. Solving Absolute Value Inequalities
Solve or

13. Solving Absolute Value Inequalities
Solve:
An absolute value must be greater than a negative number, so the set of all real numbers is the solution set to the inequality: