Solve |2x - 5| = 9; x = ?

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Prepare for the KTEST 6 2027 Test with engaging flashcards and challenging multiple choice questions. Each question comes with hints and explanations. Enhance your readiness for the exam today!

Multiple Choice

Solve |2x - 5| = 9; x = ?

Explanation:
When an absolute value equals a positive number, the expression inside can be that number or its opposite. So solve 2x - 5 = 9 and 2x - 5 = -9. - If 2x - 5 = 9, then 2x = 14, giving x = 7. - If 2x - 5 = -9, then 2x = -4, giving x = -2. Both values work: |2(7) - 5| = |14 - 5| = 9 and |2(-2) - 5| = |-4 - 5| = 9. So the solutions are x = 7 and x = -2.

When an absolute value equals a positive number, the expression inside can be that number or its opposite. So solve 2x - 5 = 9 and 2x - 5 = -9.

  • If 2x - 5 = 9, then 2x = 14, giving x = 7.

  • If 2x - 5 = -9, then 2x = -4, giving x = -2.

Both values work: |2(7) - 5| = |14 - 5| = 9 and |2(-2) - 5| = |-4 - 5| = 9. So the solutions are x = 7 and x = -2.

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