Question

which number line represents the solution set for the inequality 3(8 - 4x) < 6(x - 5)?

Explanation:

Step1: Solve the inequality

First, expand both sides:
\[

$$\begin{align*} 3(8 - 4x)&<6(x - 5)\\ 24-12x&<6x - 30 \end{align*}$$

\]
Add \(12x\) to both sides: \(24<18x - 30\).
Add 30 to both sides: \(54<18x\).
Divide both sides by 18: \(x > 3\).

Step2: Interpret the number - line representation

An open - circle at 3 and an arrow pointing to the right represents \(x>3\).

Answer:

The number - line with an open - circle at 3 and an arrow pointing to the right.