Using the properties of inequality, justify both steps in solving the inequality 25m−8<−2

To solve the inequality \( 25m - 8 < -2 \), let's break down each step, justifying them with properties of inequalities.

1. **Starting with the original inequality:**
\[
25m - 8 < -2
\]

2. **Justifying the first step:**
To isolate the term with \( m \), we add 8 to both sides of the inequality. This follows the **Addition Property of Inequalities**, which states that if \( a < b \), then \( a + c < b + c \) for any number \( c \).

Justification:
\[
25m - 8 + 8 < -2 + 8
\]
results in:
\[
25m < 6
\]

3. **Justifying the second step:**
Now, we want to isolate \( m \). To do this, we divide both sides of the inequality by 25. This follows the **Multiplication Property of Inequalities**, which states that if \( a < b \) and \( c > 0 \), then \( ac < bc \).

Note: We do not change the direction of the inequality because we are dividing by a positive number (25).

Justification:
\[
\frac{25m}{25} < \frac{6}{25}
\]
results in:
\[
m < \frac{6}{25}
\]

**Question 2: Solve for \( m \)**
\[
m < \frac{6}{25}
\]

The solution for \( m \) is:
\[
m < 0.24
\]
(since \( \frac{6}{25} = 0.24 \)).