1/4x+13>0.25(2x-32)

Solution:
1. Given inequality:
\frac{1}{4}x + 13 > 0.25(2x - 32)

2. Simplify the right side:
* Convert 0.25 to a fraction: 0.25 = \frac{1}{4}
* Distribute:
\frac{1}{4}(2x - 32) = \frac{1}{4} \cdot 2x - \frac{1}{4} \cdot 32 = \frac{1}{2}x - 8

3. Rewrite the inequality:
\frac{1}{4}x + 13 > \frac{1}{2}x - 8

4. Eliminate fractions by multiplying all terms by 4:
x + 52 > 2x - 32

5. Rearrange terms:
* Subtract x from both sides:
52 > x - 32
* Add 32 to both sides:
84 > x

6. The solution to the inequality is:
x < 84