Linear Inequalities and Absolute Value Inequalities

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Presentation transcript:

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

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.

Solving Linear Inequalities Solve

Solving Linear Inequalities Solve

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

Compound Inequalities Solve or or

Compound Inequalities Solve

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

Solving Absolute Value Inequalities Solve:

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

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

Solving Absolute Value Inequalities Solve or

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: