Using the properties of inequality, justify both steps in solving the inequality 2/5 m - 7 <= 17

To solve the inequality \( \frac{2}{5}m - 7 \leq 17 \), we can go through the steps one-by-one while justifying each operation using properties of inequalities.

1. **Add 7 to both sides**:
The first step is to eliminate the constant on the left side. We do this by adding 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**: Adding the same number to both sides of an inequality does not change the direction of the inequality.

2. **Multiply both sides by \( \frac{5}{2} \)**:
The next step is to isolate \( m \) by multiplying both sides by \( \frac{5}{2} \):
\[
m \leq 24 \times \frac{5}{2}
\]
This simplifies to:
\[
m \leq 60
\]
**Justification**: When multiplying or dividing both sides of an inequality by a positive number, the direction of the inequality remains unchanged.

Thus, after solving, we find that \( m \leq 60 \).