Question

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

Explanation:

Step1: Expand both sides

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

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

Add \(12x\) to both sides: \(24<18x - 30\). Then add \(30\) to both sides: \(24 + 30<18x\), so \(54<18x\).

Step3: Solve for \(x\)

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

Answer:

The number - line with an open circle at \(3\) and the line shaded to the right (the second option among the given ones if we assume the order as per the problem's presented options)