Using the properties of inequality, justify both steps in solving the inequality 2/5m−7≤17

To solve the inequality \( \frac{2}{5}m - 7 \leq 17 \), we will justify both steps using properties of inequalities.

### Step 1: Isolate the term with \( m \)

**Action: Add 7 to both sides of the inequality.**

\[
\frac{2}{5}m - 7 + 7 \leq 17 + 7
\]

This simplifies to:

\[
\frac{2}{5}m \leq 24
\]

**Justification:**
When we add the same value (in this case, 7) to both sides of an inequality, the direction of the inequality remains the same. This is a property of inequalities known as the "Addition Property of Inequality.”

### Step 2: Solve for \( m \)

**Action: Multiply both sides of the inequality by \( \frac{5}{2} \).**

\[
\left(\frac{5}{2}\right) \cdot \frac{2}{5}m \leq 24 \cdot \left(\frac{5}{2}\right)
\]

This simplifies to:

\[
m \leq 60
\]

**Justification:**
When multiplying both sides of an inequality by a positive number (in this case, \( \frac{5}{2} \)), the direction of the inequality remains the same. This is known as the "Multiplication Property of Inequality."

### Conclusion

Combining the justified steps, we have:

1. \( \frac{2}{5}m - 7 \leq 17 \) → Add 7: \( \frac{2}{5}m \leq 24 \)
2. Multiply by \( \frac{5}{2} \): \( m \leq 60 \)

Thus, the solution to the inequality is:

\[
m \leq 60
\]