Question

solve for ( w ) and graph the solution.

( -4 leq \frac{w - 16}{4} leq -3 )

plot the endpoints. select an endpoint to change it from closed to open. select the a segment, ray, or line to delete it.

Explanation:

Step1: Multiply all parts by 4

$$\begin{align*} -4\times4&\leq\frac{w - 16}{4}\times4\leq-3\times4\\ -16&\leq w-16\leq - 12 \end{align*}$$

Step2: Add 16 to all parts

$$\begin{align*} -16 + 16&\leq w-16 + 16\leq-12 + 16\\ 0&\leq w\leq4 \end{align*}$$

Answer:

The solution for \(w\) is \(0\leq w\leq4\). On the number - line, we plot a closed circle at \(0\) (since \(w = 0\) is included in the solution set, because of the \(\leq\) sign in \(0\leq w\)) and a closed circle at \(4\) (since \(w = 4\) is included in the solution set, because of the \(\leq\) sign in \(w\leq4\)) and then connect these two points with a line segment.