Question

1/4x-3/4 greater than 5 1/4

Answer 1

To solve the inequality \( \frac{1}{4}x - \frac{3}{4} > 5 \frac{1}{4} \), we first convert the mixed number \( 5 \frac{1}{4} \) into an improper fraction.

1. Convert \( 5 \frac{1}{4} \):
\[
5 \frac{1}{4} = \frac{5 \times 4 + 1}{4} = \frac{20 + 1}{4} = \frac{21}{4}
\]

Now the inequality becomes:
\[
\frac{1}{4}x - \frac{3}{4} > \frac{21}{4}
\]

2. Next, add \( \frac{3}{4} \) to both sides:
\[
\frac{1}{4}x > \frac{21}{4} + \frac{3}{4}
\]

3. Combine the fractions on the right:
\[
\frac{1}{4}x > \frac{21 + 3}{4} = \frac{24}{4} = 6
\]

4. Now, to isolate \( x \), we multiply both sides by 4 (note that multiplying by a positive number does not change the inequality):
\[
x > 6 \times 4
\]
\[
x > 24
\]

Thus, the solution to the inequality is:
\[
\boxed{x > 24}
\]