To solve the inequality \( 25m - 7 \leq 17 \), we can follow these steps:
### Step 1: Add 7 to both sides
By adding the same value to both sides, we maintain the direction of the inequality:
\[
25m - 7 + 7 \leq 17 + 7
\]
This simplifies to:
\[
25m \leq 24
\]
### Step 2: Divide both sides by 25
Since we are dividing both sides by a positive value, the inequality remains unchanged:
\[
\frac{25m}{25} \leq \frac{24}{25}
\]
This simplifies to:
\[
m \leq \frac{24}{25}
\]
### Conclusion
Therefore, the solution to the inequality \( 25m - 7 \leq 17 \) is:
\[
m \leq \frac{24}{25}
\]