Question

Using the properties of inequality, justify both steps in solving the inequality%C2%A0 25m−7≤17

Answer 1

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.