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 \( m < \frac{6}{25} \).
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