To solve the inequality \( 25m - 7 \leq 17 \), we will follow two steps. I'll justify each step using properties of inequalities.
### Step 1: Add 7 to both sides
**Justification:**
When we add (or subtract) the same number to both sides of an inequality, the direction of the inequality remains the same.
Here, we add 7 to both sides:
\[
25m - 7 + 7 \leq 17 + 7
\]
This simplifies to:
\[
25m \leq 24
\]
### Step 2: Divide both sides by 25
**Justification:**
When we divide (or multiply) both sides of an inequality by a positive number, the direction of the inequality remains the same.
Now, we divide both sides by 25:
\[
\frac{25m}{25} \leq \frac{24}{25}
\]
This simplifies to:
\[
m \leq \frac{24}{25}
\]
### Conclusion
So, the solution to the inequality \( 25m - 7 \leq 17 \) is:
\[
m \leq \frac{24}{25}
\]
This completes the justification for both steps in solving the inequality using the properties of inequalities.