Question

VARIABLE EQUATIONS & INEQUALITIES UNIT TEST:
USING THE PROPERTIES OF INEQUALITY, JUSTIFY BOTH STEPS IN SOLVING THE INEQUALITY \frac{2}{5}m-7\le 17.

Answer 1

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

### Step 1: Add 7 to both sides

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

This simplifies to:

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

**Justification:** Adding the same number (in this case, 7) to both sides of an inequality preserves the inequality. This is known as the Addition Property of Inequality.

### Step 2: Multiply both sides by \(\frac{5}{2}\)

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

This simplifies to:

\[
m \le 60
\]

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

### Final Result

So, the solution to the inequality \(\frac{2}{5}m - 7 \le 17\) is:

\[
m \le 60
\]