Question

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 \(18\): \(\frac{54}{18} 3\).

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).