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To solve the inequality \( \frac{4}{5}d \leq 24 \), we start by isolating \( d \).
1. Multiply both sides of the inequality by \( \frac{5}{4} \) to eliminate the fraction. Note that since \( \frac{5}{4} \) is positive, the direction of the inequality remains the same:
\[
d \leq 24 \times \frac{5}{4}
\]
2. Calculate \( 24 \times \frac{5}{4} \):
\[
24 \times \frac{5}{4} = 24 \div 4 \times 5 = 6 \times 5 = 30
\]
3. Thus, we have:
\[
d \leq 30
\]
The solution to the inequality is \( d \leq 30 \).