Question

solve the inequality. graph the solution set and write it in interval notat
2 ≤ 3x - 10 ≤ 8

choose the correct graph below.

a.

c.

write the solution in interval notation.

(type your answer in interval notation.)

Explanation:

Step1: Solve the inequality

$$\begin{align*} 2&\leq3x - 10\leq8\\ 2+10&\leq3x-10 + 10\leq8 + 10\\ 12&\leq3x\leq18\\ \frac{12}{3}&\leq\frac{3x}{3}\leq\frac{18}{3}\\ 4&\leq x\leq6 \end{align*}$$

Step2: Analyze the graph

The solution \(4\leq x\leq6\) means the graph should have closed - end points at \(x = 4\) and \(x=6\) and a line segment between them.

Step3: Write in interval notation

The interval notation for \(4\leq x\leq6\) is \([4,6]\)

Answer:

The correct graph is not fully described in the options (assuming the correct graph has closed - circles at \(4\) and \(6\) and a line between them). The solution in interval notation is \([4,6]\)