Question

current skill solve and graph the following inequality: $-3 \leq 4x + 9 \leq 8$ inequality: graph:

Explanation:

Step1: Subtract 9 from all parts

$$\begin{align*} -3 - 9&\leq4x+9 - 9\leq8 - 9\\ -12&\leq4x\leq - 1 \end{align*}$$

Step2: Divide all parts by 4

$$\begin{align*} \frac{-12}{4}&\leq\frac{4x}{4}\leq\frac{-1}{4}\\ -3&\leq x\leq-\frac{1}{4} \end{align*}$$

Answer:

The solution of the inequality is \(-3\leq x\leq-\frac{1}{4}\). To graph it, draw a number line. Put a closed circle at \(-3\) (because \(x = - 3\) is included in the solution, due to the \(\leq\) sign) and a closed circle at \(-\frac{1}{4}\) (because \(x=-\frac{1}{4}\) is included in the solution). Then shade the region between these two points.