Question

solve and graph the following inequality: $-7 leq 6x - 9$
inequality:
graph:

Explanation:

Step1: Add 9 to both sides

$$\begin{align*} -7+9&\leq6x - 9+9\\ 2&\leq6x \end{align*}$$

Step2: Divide both sides by 6

$$\begin{align*} \frac{2}{6}&\leq\frac{6x}{6}\\ \frac{1}{3}&\leq x \end{align*}$$

Answer:

The inequality is \(x\geq\frac{1}{3}\). To graph it, place a closed - circle at \(\frac{1}{3}\) on the number line (because the inequality is \(\geq\)) and shade to the right of \(\frac{1}{3}\).