Solve the equation |2x - 5| = 3.

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

Solve the equation |2x - 5| = 3.

Explanation:
An absolute value equation equals a number only when the inside expression is that number or its opposite. So for |2x − 5| = 3, the inside 2x − 5 must be either 3 or −3. Solving 2x − 5 = 3 gives x = 4, and solving 2x − 5 = −3 gives x = 1. Therefore the solutions are x = 1 and x = 4. You can check: |2(1) − 5| = |−3| = 3 and |2(4) − 5| = |3| = 3. The other candidate values don’t work because they don’t make the left-hand side equal to 3.

An absolute value equation equals a number only when the inside expression is that number or its opposite. So for |2x − 5| = 3, the inside 2x − 5 must be either 3 or −3. Solving 2x − 5 = 3 gives x = 4, and solving 2x − 5 = −3 gives x = 1. Therefore the solutions are x = 1 and x = 4. You can check: |2(1) − 5| = |−3| = 3 and |2(4) − 5| = |3| = 3. The other candidate values don’t work because they don’t make the left-hand side equal to 3.

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