Question

Solve the following inequality and justify each step with a property of inequality. 25m − 7 ≤17

Answer 1

So the answer is

Answer 2

To solve the inequality \( 25m - 7 \leq 17 \), we'll go through the steps and justify each step with properties of inequalities.

### Step 1: Add 7 to both sides
To isolate the term with \( m \), we'll add 7 to both sides of the inequality.

\[
25m - 7 + 7 \leq 17 + 7
\]
\[
25m \leq 24
\]

*Justification: Adding the same number (in this case, 7) to both sides of an inequality preserves the inequality.*

### Step 2: Divide both sides by 25
Now, we divide both sides by 25 to solve for \( m \).

\[
\frac{25m}{25} \leq \frac{24}{25}
\]
\[
m \leq \frac{24}{25}
\]

*Justification: Dividing both sides of an inequality by a positive number (here, 25) preserves the inequality.*

### Conclusion
The solution to the inequality \( 25m - 7 \leq 17 \) is

\[
m \leq \frac{24}{25}
\]

This means that \( m \) can take any value that is less than or equal to \( \frac{24}{25} \).

Answer 3

The solution to the inequality \( 25m - 7 \leq 17 \) is

\[
m \leq \frac{24}{25}.
\]

This means that \( m \) can be any value that is less than or equal to \( \frac{24}{25} \).