Question

solve and graph the inequality. -169 ≤ 8m - 9

Explanation:

Step1: Add 9 to both sides

To isolate the term with \( m \), we add 9 to both sides of the inequality \(-169 \leq 8m - 9\). This gives us \(-169 + 9 \leq 8m - 9 + 9\), which simplifies to \(-160 \leq 8m\).

Step2: Divide both sides by 8

To solve for \( m \), we divide both sides of the inequality \(-160 \leq 8m\) by 8. This gives us \(\frac{-160}{8} \leq \frac{8m}{8}\), which simplifies to \(-20 \leq m\) or \( m \geq -20 \).

Answer:

The solution to the inequality is \( m \geq -20 \). To graph this, we draw a number line, place a closed circle at \(-20\) (since the inequality is "greater than or equal to"), and draw an arrow to the right to represent all values of \( m \) greater than or equal to \(-20\).