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Algebra II Recipe: Solving Absolute Value Equations and Inequalities
A. Solving Absolute Value Equations
  1. Isolate the absolute value.
  2. Write a compound sentence with "OR" between the two sentences.
  3. Solve each sentence or equation.
  4. Check each solution where the absolute value is isolated.
  5. The answer is No Solution if neither number produces a true statement when checked.
ExamplesExamples:
|2x - 7| - 5 = 4
6 - 5|x - 1| = 1
B. Solving Absolute Value Inequalities
  1. Isolate the absolute value.
  2. Write the 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 symbols.
    • Sentence 2 looks like sentence 1, EXCEPT, change (flip) the inequality symbol and change the value on the right to its opposite.
  3. Solve each sentence or inequality.
  4. Graph the solution.
ExamplesExamples:
|3x - 15| < 15
|4 - x| ≥ 2



G Redden

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