Question

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

Explanation:

Step1: Expand both sides

First, expand \(3(8 - 4x)\) and \(6(x - 5)\).
\[3\times8-3\times4x<6x-6\times5\]
\[24 - 12x<6x - 30\]

Step2: Add \(12x\) to both sides

To get the \(x\) - terms on one side, add \(12x\) to both sides of the inequality.
\[24-12x + 12x<6x-30 + 12x\]
\[24<18x - 30\]

Step3: Add 30 to both sides

To isolate the term with \(x\), add 30 to both sides.
\[24 + 30<18x-30 + 30\]
\[54<18x\]

Step4: Divide both sides by 18

To solve for \(x\), divide both sides by 18.
\[\frac{54}{18}<\frac{18x}{18}\]
\[3 3\)

The solution set on a number - line is represented by an open circle at 3 and an arrow pointing to the right.

Answer:

The second number - line (the one with an open circle at 3 and an arrow pointing to the right) represents the solution set.