Question

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

Explanation:

Step1: Expand the inequality

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

Step2: Move the terms with \(x\) to one side

Add \(12x\) to both sides: \(24<18x - 30\)

Step3: Isolate the term with \(x\)

Add \(30\) to both sides: \(24 + 30<18x\), so \(54<18x\)

Step4: Solve for \(x\)

Divide both sides by \(18\): \(x > 3\)

On a number - line, for \(x>3\), there is an open circle at \(x = 3\) (since \(x
eq3\)) and the arrow points to the right (towards larger values of \(x\))

Answer:

The number - line with an open circle at \(3\) and an arrow pointing to the right represents the solution set.