Question

graph the solution of the inequality $-10leq5x + 20lt30$ 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:

The solution is \( -6\leq x < 2\). On the number - line, we use a closed circle at \(x = - 6\) (because of the \(\leq\) sign) and an open circle at \(x = 2\) (because of the \(<\) sign) and shade the region between them.