Objective:

To solve and graph compound inequalities.

Vocabulary:

Notes:

Solving absolute value inequalities:
  1. Isolate the absolute value part (Get the absolute value part alone).
  2. Decide if the problem is a conjunction or a disjunction
    • Conjunction - The form is like |x| < 7
      • I call this a less and problem (almost rhymes with 'less than').
      • Write this problem as a long conjoined problem −7 < x < 7
      • Solve the problem like you would a normal inequality.
      • Remember that you have three sides - what you do to one side you do to all.
    • Disjunction - The form is like |x| > 7
      • I call this a great or problem (almost rhymes with 'greater').
      • Write this problem as two separate problems x > 7and x < −7
      • Notice that the inequality symbol is switched and the sign is changed to negative on the second problem.
  3. Solve your rewritten inequality or inequalities.

Examples:

Solve:

Solve each inequality.

  1. |x + 9| > 13

    Ex 1


  2. |3x − 15| < 12

    Ex 2


  3. |10 − 4x| < 2

    Ex 3

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This page was last updated on 08/09/13.