1.7 Solving Absolute Value Equations
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This document discusses how to solve absolute value equations and inequalities. It explains that absolute value equations can have two solutions that come from setting the expression equal to the number or its opposite. It provides examples of solving equations of the form |ax + b| = c by writing it as two separate equations. The document also explains how to solve absolute value inequalities by rewriting them as compound inequalities using "and" or "or", depending on whether the inequality sign is < or >, and then solving the resulting inequalities.
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1.7 Solving Absolute Value Equations
- 1. 1.7 Solving Absolute Value Equations
- 2. Solving an Absolute Value Equation • Absolute value equations can have two solutions. • For example, |x| = 5 could have solutions x = 5 or x = -5 • To solve |ax + b| = c, write as two equations: ax + b = c or ax + b = -c, then solve both.
- 3. Example: • Solve |2x – 5| = 9
- 4. Example: • Solve |x – 3| = -4
- 5. Your Turn! • Solve |6x – 3| = 15
- 6. Solving Inequalities: |ax + b| c • |ax + b| c means ax + b is between –c and c • Rewrite as an “and” compound inequality, then solve. -c < ax + b < c
- 7. Example: • Solve |2x + 7| < 11 and graph the solution on a number line.
- 8. Your Turn! • Solve |-x + 5| 6 and graph the solution.
- 9. Solving Inequalities: |ax + b| > c • |ax + b| > c means ax + b is beyond –c and c • Rewrite as an “or” compound inequality, then solve. ax + b < -c or ax + b > c
- 10. Example: • Solve |3x – 2| 8 and graph the solution.
- 11. Your Turn! • Solve |x + 5| > 12 and graph the solution.