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Algebra I Recipe: Solving Absolute Value Inequalities
Steps
  1. Isolate the absolute value using inverse operations.
  2. Write a compound sentence.
    • With “AND” if you have <  or  ≤ after isolating.
    • With “OR” if you have >  or  ≥ after isolating
    • Sentence 1 – is the isolated inequality without the absolute value bars
    • Sentence 2 – looks like sentence 1 except change the inequality symbol and change the number on the right to it’s opposite.
  3. Solve each sentence (inequality) for the variable.
  4. Graph the solution.
ExamplesExamples:
| 3x - 15| < 12
| 4 - x | ≥  2
| 5x + 1 | - 8  ≤  16
| 2x + 5 | - 1 < 6
| 3x + 2 | - 1  ≥  10



G Redden

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