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# 1.6 Equations & Inequalities Absolute Value

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• 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.