Question

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

25m−8+8<−2+8


52(25m)<52(6)


Question 2
Solve for m
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Answers

GPT-4o mini
To solve the inequality \( 25m - 8 < -2 \), we proceed step by step while justifying each step based on the properties of inequalities.

### Step 1: Isolate the term containing \( m \)
We start with the original inequality:

\[
25m - 8 < -2
\]

To isolate \( 25m \), we add \( 8 \) to both sides of the inequality. This step is justified by the property of inequalities that states if \( a < b \), then \( a + c < b + c \) for any real number \( c \).

\[
25m - 8 + 8 < -2 + 8
\]

This simplifies to:

\[
25m < 6
\]

### Step 2: Solve for \( m \)
Next, we want to solve for \( m \). To do this, we divide both sides of the inequality by \( 25 \). This is justified by the property of inequalities that states if \( a < b \) and \( c > 0 \), then \( \frac{a}{c} < \frac{b}{c} \).

\[
\frac{25m}{25} < \frac{6}{25}
\]

This simplifies to:

\[
m < \frac{6}{25}
\]

### Final Solution
Thus, the solution to the inequality is:

\[
m < \frac{6}{25}
\]

In conclusion, both steps involve properties of inequalities, namely the addition property (adding the same value to both sides) and the division property (dividing both sides by a positive number). The final answer is \( m < \frac{6}{25} \).