Using the properties of inequality, justify both steps in solving the inequality 2/5m−7≤17 .(4 points)

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

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

Start 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 (in this case, \( 7 \)) to both sides of an inequality maintains the inequality. This is known as the **Addition Property of Inequality**.

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

Next, multiply both sides of the inequality by \( \frac{5}{2} \):

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

This simplifies to:

\[
m \leq 60
\]

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

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Thus, the final solution to the inequality is:

\[
m \leq 60
\]

These steps showed how we used properties of inequalities to justify our operations while solving for \( m \).