Question

solve the inequality and graph the solution
8(z - 2) - 6 < 10
plot the endpoints. select an endpoint to change it from closed to open. select the
middle of the segment, ray, or line to delete it.

Explanation:

Step1: Simplify the inequality

$$\begin{align*} 8(z - 2)-6&<10\\ 8z-16 - 6&<10\\ 8z-22&<10 \end{align*}$$

Step2: Isolate the variable term

Add \(22\) to both sides of the inequality:

$$\begin{align*} 8z-22 + 22&<10+ 22\\ 8z&<32 \end{align*}$$

Step3: Solve for \(z\)

Divide both sides by \(8\):

$$\begin{align*} \frac{8z}{8}&<\frac{32}{8}\\ z&<4 \end{align*}$$

Answer:

The solution of the inequality \(8(z - 2)-6<10\) is \(z < 4\). On the number - line, we plot an open circle at \(4\) (because the inequality is strict, \(z
eq4\)) and draw a ray to the left of \(4\) (since \(z\) is less than \(4\)).