Question

graph the solution of the inequality $-10 leq 5x + 20 < 30$ on the number line below.

Explanation:

Step1: Subtract 20 from all parts

$$\begin{align*} -10 - 20&\leq5x+20 - 20<30 - 20\\ -30&\leq5x<10 \end{align*}$$

Step2: Divide all parts by 5

$$\begin{align*} \frac{-30}{5}&\leq\frac{5x}{5}<\frac{10}{5}\\ -6&\leq x<2 \end{align*}$$

Answer:

On the number - line, we use a closed circle at \(x = - 6\) (because \(x=-6\) is included in the solution, due to the \(\leq\) sign) and an open circle at \(x = 2\) (because \(x = 2\) is not included in the solution, due to the \(<\) sign), and shade the region between them.