To solve the inequality \( \frac{x}{8} > 4 \), follow these steps:
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Multiply both sides by 8 to eliminate the fraction. Since we are multiplying by a positive number, the direction of the inequality remains the same:
\[ x > 4 \times 8 \]
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Perform the multiplication:
\[ x > 32 \]
Thus, the solution to the inequality is:
\[ x > 32 \]