Question

solve for h and graph the solution. -3 ≤ (4h + 11)/3 < 5 plot the endpoints. select an endpoint to change it from closed to open. select the middle of a segment, ray, or line to delete it.

Explanation:

Step1: Multiply all parts by 3

\[

$$\begin{align*} -3\times3&\leq\frac{4h + 11}{3}\times3<5\times3\\ -9&\leq4h + 11<15 \end{align*}$$

\]

Step2: Subtract 11 from all parts

\[

$$\begin{align*} -9-11&\leq4h+11 - 11<15 - 11\\ -20&\leq4h<4 \end{align*}$$

\]

Step3: Divide all parts by 4

\[

$$\begin{align*} \frac{-20}{4}&\leq\frac{4h}{4}<\frac{4}{4}\\ - 5&\leq h<1 \end{align*}$$

\]

Answer:

The solution for \(h\) is \(-5\leq h<1\). On the number - line, we plot a closed circle at \(-5\) (because the inequality includes equality for this end - point) and an open circle at \(1\) (because the inequality is strict for this end - point), and draw a line segment connecting them.