Problem

Solve the absolute value equation: \( |2x - 3| = 5 \)

Answer

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Answer

Solving the second equation gives: \(2x = -5 + 3\) which simplifies to \(2x = -2\). Dividing each side by 2 gives \(x = -1\)

Steps

Step 1 ：Rewrite the absolute value equation as two separate equations: \(2x - 3 = 5\) and \(2x - 3 = -5\)

Step 2 ：Solving the first equation gives: \(2x = 5 + 3\) which simplifies to \(2x = 8\). Dividing each side by 2 gives \(x = 4\)

Step 3 ：Solving the second equation gives: \(2x = -5 + 3\) which simplifies to \(2x = -2\). Dividing each side by 2 gives \(x = -1\)

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