Solve |2x - 5| = 7 – Step-by-Step Solution

Answer

\boxed{x = 6, \text{ } x = -1}

Substituting both values back into the original equation yields $|2(6) - 5| = |7| = 7$ and $|2(-1) - 5| = |-7| = 7$ , confirming both solutions are correct.

Problem: Solve the absolute value equation $|2x - 5| = 7$ .

Steps

Split into two cases $2x - 5 = 7 \quad \text{or} \quad 2x - 5 = -7$
Add 5 to both sides of both equations $2x = 12 \quad \text{or} \quad 2x = -2$
Divide both sides by 2 $x = 6 \quad \text{or} \quad x = -1$

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Solve |2x - 5| = 7

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