To solve the inequality \( \frac{1}{4}x - \frac{3}{4} > 5 \frac{1}{4} \), first convert \( 5 \frac{1}{4} \) into an improper fraction:
\[ 5 \frac{1}{4} = 5 + \frac{1}{4} = \frac{20}{4} + \frac{1}{4} = \frac{21}{4} \]
Now replace \( 5 \frac{1}{4} \) in the original inequality:
\[ \frac{1}{4}x - \frac{3}{4} > \frac{21}{4} \]
Next, add \( \frac{3}{4} \) to both sides:
\[ \frac{1}{4}x > \frac{21}{4} + \frac{3}{4} \] \[ \frac{1}{4}x > \frac{24}{4} \] \[ \frac{1}{4}x > 6 \]
Now, multiply both sides by \( 4 \) to eliminate the fraction:
\[ x > 24 \]
So the solution to the inequality is:
\[ x > 24 \]
The correct response is: x > 24.