To solve the inequality \( 12 - \frac{2}{3}x > 6 \), follow these steps:
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Isolate the variable term: Start by subtracting 12 from both sides.
\[ 12 - \frac{2}{3}x - 12 > 6 - 12 \]
This simplifies to:
\[ -\frac{2}{3}x > -6 \]
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Eliminate the negative coefficient: To make the coefficient of \( x \) positive, multiply both sides of the inequality by -1. Remember to flip the inequality sign when you do this.
\[ \frac{2}{3}x < 6 \]
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Solve for \( x \): To get \( x \) by itself, multiply both sides by the reciprocal of \( \frac{2}{3} \), which is \( \frac{3}{2} \):
\[ x < 6 \cdot \frac{3}{2} \]
Calculate \( 6 \cdot \frac{3}{2} \):
\[ 6 \cdot \frac{3}{2} = \frac{18}{2} = 9 \]
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Final result: Thus, the solution to the inequality is:
\[ x < 9 \]
This tells us that \( x \) can take any value less than 9.
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