Question

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

Explanation:

Step1: Subtract 2 from both sides

Subtract 2 from each side of the inequality \(-8n + 2 \leq 50\) to isolate the term with \(n\).
\(-8n + 2 - 2 \leq 50 - 2\)
Simplify: \(-8n \leq 48\)

Step2: Divide by -8 (reverse inequality)

Divide both sides by \(-8\). When dividing an inequality by a negative number, reverse the inequality sign.
\(\frac{-8n}{-8} \geq \frac{48}{-8}\)
Simplify: \(n \geq -6\)

Answer:

The solution to the inequality \(-8n + 2 \leq 50\) is \(n \geq -6\). For the graph, on a number line, draw a closed circle at \(-6\) (since the inequality includes equality) and shade to the right of \(-6\) to represent all values of \(n\) greater than or equal to \(-6\).