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To solve the equation \( |5(3-2 x)|=6 \), we start by breaking it into two cases because of the absolute value. **Case 1:** \( 5(3 - 2x) = 6 \) Dividing both sides by 5 gives us: \[ 3 - 2x = \frac{6}{5} \] Now, rearranging for \( x \): \[ -2x = \frac{6}{5} - 3 \quad \Rightarrow \quad -2x = \frac{6}{5} - \frac{15}{5} = \frac{-9}{5} \] Dividing by -2: \[ x = \frac{-9}{5} \cdot \frac{-1}{2} = \frac{9}{10} \] **Case 2:** \( 5(3 - 2x) = -6 \) Again, divide both sides by 5: \[ 3 - 2x = -\frac{6}{5} \] Rearranging gives us: \[ -2x = -\frac{6}{5} - 3 \quad \Rightarrow \quad -2x = -\frac{6}{5} - \frac{15}{5} = -\frac{21}{5} \] Dividing by -2: \[ x = \frac{21}{5} \cdot \frac{-1}{2} = \frac{-21}{10} \] Thus, the solutions to the equation are: \[ x = \frac{9}{10} \quad \text{and} \quad x = -\frac{21}{10} \]
