Question

1. graph the solution to the inequality.

-\frac{1}{3}x \geq 2 or 2(x + 1) > 8

Explanation:

Step1: Solve the first inequality

Multiply both sides of \(-\frac{1}{3}x\geq2\) by \(-3\). Remember to reverse the inequality sign when multiplying by a negative number.
\(x\leq - 6\)

Step2: Solve the second inequality

First, distribute the \(2\) in \(2(x + 1)>8\): \(2x+2>8\). Then subtract \(2\) from both sides: \(2x>6\). Divide both sides by \(2\): \(x > 3\)

Answer:

To graph \(x\leq - 6\), draw a closed circle at \(-6\) (because the inequality includes equality) and shade to the left. To graph \(x>3\), draw an open circle at \(3\) (because the inequality does not include equality) and shade to the right.