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

Explanation:

Step1: Expand both sides

Expand (3(8 - 4x)) to get (24-12x), and expand (6(x - 5)) to get (6x-30). So the inequality becomes (24-12x<6x - 30).

Step2: Move variables to one side

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

Step3: Move constants 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 (3<x) or (x > 3).

Answer:

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