Question

solve and graph the following inequality: 2 + 9x ≤ -6

Explanation:

Step1: Simplify the inequality

$$\begin{align*} 2 + 9x&\leq-6\\ 9x&\leq-6 - 2\\ 9x&\leq-8 \end{align*}$$

Step2: Solve for \(x\)

Divide both sides by \(9\): \(x\leq-\frac{8}{9}\)

Answer:

The solution of the inequality \(2 + 9x\leq-6\) is \(x\leq-\frac{8}{9}\). On the number - line, we represent it with a closed circle at \(-\frac{8}{9}\) (because the inequality is \(\leq\)) and an arrow pointing to the left (towards the smaller numbers).