To solve the inequality \( 25m - 7 \leq 17 \), we proceed with the following steps:
### Step 1: Add 7 to both sides
Adding the same number to both sides maintains the inequality's direction:
\[
25m - 7 + 7 \leq 17 + 7
\]
This simplifies to:
\[
25m \leq 24
\]
### Step 2: Divide both sides by 25
Dividing both sides by a positive number preserves the inequality:
\[
\frac{25m}{25} \leq \frac{24}{25}
\]
This simplifies to:
\[
m \leq \frac{24}{25}
\]
### Conclusion
Thus, the solution to the inequality \( 25m - 7 \leq 17 \) is:
\[
m \leq \frac{24}{25}
\]