The document discusses solving equations and inequalities involving absolute value. It defines absolute value as the distance from a number to zero, and explains that absolute value equations can be solved by setting the expression equal to the absolute value or its negative. Absolute value inequalities are solved by splitting them into two inequalities and solving each part separately, with different approaches for less than or greater than cases. Examples are provided for both types of problems.

1. College Algebra 1.6 Equations & Inequalities Involving Absolute Value

2. Absolute Value Equations │ U│ = the distance from U to 0. │ -8│ = the distance from -8 to 0. Henceforth, │-8│ = ____ Solve │x│ = 3. In other words: The absolute value of what number(s) is 3? • Solve │x│ = 3. ↔ x = ____ or x = ____ Check this.

3. Solving Absolute Value Equations │ U│ = a ↔ YOU MUST CONVERT THE ABOVE EQUATION TO THESE 2 EQUATIONS! U = ____ or U = _____ If a is a positive real number and if u is any algebraic expression, then

4. c) │x - 5│ = 17. d) │ │ = 1.

5. Solving Absolute Value Inequalities ( Less Than ) First plot the solutions.

6. Solve Solving Absolute Value Inequalities ( Less Than ) 1. Write: –c ≤ ax + b ≤ c 2. Solve the compound inequality.

7. Solving Absolute Value Inequalities ( Greater Than ) First plot the solutions.

8. Solve Solving Absolute Value Inequalities ( Greater Than ) 1. Write: ax + b ≥ c OR ax + b ≤ -c 2. Solve each inequality.

9. Review Absolute Value Inequalities │ U│ < a ↔ _______________________ │ U│ ≥ a ↔ _______________________ Examples: 1. Solve │1 – 6x│ < 7. 2. Solve –│1 – 2x│ ≤ – 3.