Question

which number line represents the solution set for the inequality ( 3(8 - 4x) lt 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

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

Step3: Isolate the term with \(x\)

Add \(30\) to both sides: \(54<18x\)

Step4: Solve for \(x\)

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

Answer:

The number line with an open circle at \(3\) and shading to the right (the second option among the given choices).