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1.6 Equations & Inequalities   Absolute Value
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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.