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# 1.6 Equations & Inequalities Absolute Value

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### 1.6 Equations & Inequalities Absolute Value

1. 1. College Algebra 1.6 Equations & Inequalities Involving Absolute Value
2. 2. Absolute Value Equations <ul><li>│ U│ = the distance from U to 0. </li></ul><ul><li>│ -8│ = the distance from -8 to 0. </li></ul><ul><li>Henceforth, │-8│ = ____ </li></ul><ul><li>Solve │x│ = 3. In other words: </li></ul><ul><li>The absolute value of what number(s) is 3? </li></ul><ul><li>• Solve │x│ = 3. ↔ x = ____ or x = ____ </li></ul><ul><li>Check this. </li></ul>
3. 3. Solving Absolute Value Equations <ul><li>│ U│ = a ↔ </li></ul><ul><li>YOU MUST CONVERT THE ABOVE </li></ul><ul><li>EQUATION TO THESE 2 EQUATIONS! </li></ul><ul><li>U = ____ or U = _____ </li></ul>If a is a positive real number and if u is any algebraic expression, then
4. 4. c) │x - 5│ = 17. d) │ │ = 1.
5. 5. Solving Absolute Value Inequalities ( Less Than ) First plot the solutions.
6. 6. <ul><li>Solve </li></ul>Solving Absolute Value Inequalities ( Less Than ) 1. Write: –c ≤ ax + b ≤ c 2. Solve the compound inequality.
7. 7. Solving Absolute Value Inequalities ( Greater Than ) First plot the solutions.
8. 8. <ul><li>Solve </li></ul>Solving Absolute Value Inequalities ( Greater Than ) 1. Write: ax + b ≥ c OR ax + b ≤ -c 2. Solve each inequality.
9. 9. Review Absolute Value Inequalities <ul><li>│ U│ < a ↔ _______________________ </li></ul><ul><li>│ U│ ≥ a ↔ _______________________ </li></ul><ul><li>Examples: </li></ul><ul><li>1. Solve │1 – 6x│ < 7. </li></ul><ul><li>2. Solve –│1 – 2x│ ≤ – 3. </li></ul>