Problem

Solve the equation \(\left| 5x - 3 \right| = 7\).

Answer

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Answer

Solving the second equation \(5x - 3 = -7\), we get \(5x = -7 + 3\), then \(5x = -4\), which implies \(x = \frac{-4}{5} = -0.8\).

Steps

Step 1 ：The absolute value equation \(\left| 5x - 3 \right| = 7\) means that \(5x - 3 = 7\) or \(5x - 3 = -7\).

Step 2 ：Solving the first equation \(5x - 3 = 7\), we get \(5x = 7 + 3\), then \(5x = 10\), which implies \(x = \frac{10}{5} = 2\).

Step 3 ：Solving the second equation \(5x - 3 = -7\), we get \(5x = -7 + 3\), then \(5x = -4\), which implies \(x = \frac{-4}{5} = -0.8\).

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