Solving absolute value inequalities

Solving absolute value inequalities

Lessons

\bullet absolute value inequalities: | \heartsuit | < aa,
solution:a-a < \heartsuit < aa
\bullet absolute value inequalities: | \heartsuit | > aa,
solution:\heartsuit < a-a or\;or\; \heartsuit > aa
  • 1.
    \bullet definition of absolute value: = | \heartsuit | = distance of \heartsuit from zero
    \bullet absolute value inequalities: | \heartsuit | < aa,
    solution:a-a < \heartsuit < aa
    \bullet absolute value inequalities: | \heartsuit | > aa,
    solution:\heartsuit < a-a or\;or\; \heartsuit > aa

  • 2.
    Solving Basic Absolute Value Inequalities
    Solve:
    a)
    x |x| < 44
    x|x| \leq 44

    b)
    x |x| > 44
    x |x| \geq 44


  • 3.
    Solving Absolute Value Inequalities Involving “less than”
    Solve: 2x1 |2x-1| < 33

  • 4.
    Solving Absolute Value Inequalities Involving “greater than”
    Solve:
    a)
    4x5 |4x-5| > 77

    b)
    x51 |x|-5 \geq -1


  • 5.
    Multiplying/Dividing an Inequality by a Negative Number
    Solve:
    a)
    32x11 |3-2x| \leq 11

    b)
    x6+53 |-\frac{x}{6}+\frac{5}{3}| > 22


  • 6.
    Given a Pair of Inequalities, Determine the Corresponding Absolute Value Inequality
    Determine the absolute value inequality statement that corresponds to each inequality:
    a)
    1-1 < xx < 55

    b)
    x10 x \leq-10 or\;or\; x2x \geq 2


  • 7.
    Recognizing Absolute Value Inequalities with “No Solution” or “All Real Numbers”
    Solve:
    a)
    x+3 |x+3| < 5-5

    b)
    x4 |x-4| > 1-1