Solving absolute value inequalities

All in One Place

Everything you need for better grades in university, high school and elementary.

Learn with Ease

Made in Canada with help for all provincial curriculums, so you can study in confidence.

Instant and Unlimited Help

Get the best tips, walkthroughs, and practice questions.

0/1
?
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
0/11
?
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
    ?
    \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