Solving absolute value inequalities

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Intros
Lessons
  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
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Examples
Lessons
  1. Solving Basic Absolute Value Inequalities
    Solve:
    1. x |x| < 44
      x|x| \leq 44
    2. x |x| > 44
      x |x| \geq 44
  2. Solving Absolute Value Inequalities Involving "less than"
    Solve: 2x1 |2x-1| < 33
    1. Solving Absolute Value Inequalities Involving "greater than"
      Solve:
      1. 4x5 |4x-5| > 77
      2. x51 |x|-5 \geq -1
    2. Multiplying/Dividing an Inequality by a Negative Number
      Solve:
      1. 32x11 |3-2x| \leq 11
      2. x6+53 |-\frac{x}{6}+\frac{5}{3}| > 22
    3. Given a Pair of Inequalities, Determine the Corresponding Absolute Value Inequality
      Determine the absolute value inequality statement that corresponds to each inequality:
      1. 1-1 < xx < 55
      2. x10 x \leq-10   or  \;or\; x2x \geq 2
    4. Recognizing Absolute Value Inequalities with "No Solution" or "All Real Numbers"
      Solve:
      1. x+3 |x+3| < 5-5
      2. x4 |x-4| > 1-1
    Topic Notes
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    \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