To solve the inequality \( 12 - \frac{2}{3}x > 6 \), follow these steps:
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Subtract 12 from both sides: \[ -\frac{2}{3}x > 6 - 12 \] \[ -\frac{2}{3}x > -6 \]
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To isolate \( x \), multiply both sides by -3/2. Remember that when you multiply or divide by a negative number, you need to flip the inequality sign: \[ x < -6 \cdot \left(-\frac{3}{2}\right) \] \[ x < 9 \]
The solution to the inequality is: \[ x < 9 \]