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

Explanation:

Step1: Expand both sides

Expanding gives $24 - 12x<6x - 30$.

Step2: Move x - terms to one side

Add $12x$ to both sides: $24<6x + 12x-30$, which simplifies to $24<18x - 30$.

Step3: Move constant terms to one side

Add 30 to both sides: $24 + 30<18x$, so $54<18x$.

Step4: Solve for x

Divide both sides by 18: $\frac{54}{18}<x$, which gives $x > 3$.

Answer:

The number - line with an open - circle at 3 and an arrow pointing to the right (the second option in the given choices).