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.