Question

practice

1. solve -8m + 2 ≤ 50. then graph the solution.

Explanation:

Step1: Subtract 2 from both sides

To isolate the term with \( m \), we subtract 2 from both sides of the inequality \(-8m + 2 \leq 50\). This gives us \(-8m + 2 - 2 \leq 50 - 2\), which simplifies to \(-8m \leq 48\).

Step2: Divide by -8 (reverse inequality)

When dividing an inequality by a negative number, we must reverse the inequality sign. So, dividing both sides of \(-8m \leq 48\) by \(-8\) gives \( m \geq \frac{48}{-8}\), which simplifies to \( m \geq -6 \).

Step3: Graph the solution

On a number line, we represent \( m \geq -6 \) by placing a closed circle (since the inequality is "greater than or equal to") at \(-6\) and drawing an arrow to the right (indicating all numbers greater than or equal to \(-6\)).

Answer:

The solution to the inequality \(-8m + 2 \leq 50\) is \( m \geq -6 \). The graph has a closed circle at \(-6\) and an arrow pointing to the right.