Question

solve and graph the following inequality: $-1\leq7x + 9$

Explanation:

Step1: Subtract 9 from both sides

$$\begin{align*} -1-9&\leq7x + 9-9\\ -10&\leq7x \end{align*}$$

Step2: Divide both sides by 7

$$\begin{align*} \frac{-10}{7}&\leq\frac{7x}{7}\\ -\frac{10}{7}&\leq x \end{align*}$$

Answer:

The solution of the inequality is \(x\geq-\frac{10}{7}\). On the number - line, we draw a closed circle at \(x =-\frac{10}{7}\) (because the inequality includes equality, \(\leq\)) and shade to the right of \(x =-\frac{10}{7}\).