Question

which number line represents the solution set for this inequality?
8x - 12 ≤ 12

Explanation:

Step1: Solve the inequality for \(x\)

Add \(12\) to both sides of \(8x - 12\leq12\):
\(8x-12 + 12\leq12 + 12\), which simplifies to \(8x\leq24\).

Step2: Isolate \(x\)

Divide both sides of \(8x\leq24\) by \(8\): \(\frac{8x}{8}\leq\frac{24}{8}\), so \(x\leq3\).

On a number - line, \(x\leq3\) is represented by a closed circle at \(3\) (because the inequality includes equality, i.e., \(x = 3\) is part of the solution set) and a line extending to the left.

Answer:

The number - line with a closed circle at \(3\) and a line extending to the left.