Question

Which number line represents the solution set for the inequality 2x – 6 ≥ 6(x – 2) + 8?

A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at 0.5 and a bold line starts at 0.5 and is pointing to the left.
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at 0.5 and a bold line starts at 0.5 and is pointing to the right.
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at negative 0.5 and a bold line starts at negative 0.5 and is pointing to the left.
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at negative 0.5 and a bold line starts at negative 0.5 and is pointing to the right.

Answer 1

Solve: 2x − 6 ≥ 6(x − 2) + 8
RHS = 6x − 12 + 8 = 6x − 4
So 2x − 6 ≥ 6x − 4 ⇒ −4x − 6 ≥ −4 ⇒ −4x ≥ 2 ⇒ x ≤ −1/2.

So the number line with a closed point at −0.5 and the ray pointing left (x ≤ −0.5) is correct — the third option.