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

b

Explanation:

Answer 2

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 negative 0.5 and is pointing to the left.

Explanation:

Required

`2x - 6 \geq 6(x - 2) + 8`

Required

Determine the number line

`2x - 6 \geq 6(x - 2) + 8`

Open the bracket

`2x - 6 \geq 6*x - 6*2 + 8`

`2x - 6 \geq 6x - 12 + 8`

`2x - 6 \geq 6x - 4`

Collect Like Terms

`2x - 6x \geq 6 - 4`

`- 4x \geq 2`

Divide both sides by -4

`(- 4x)/(-4) \geq (2)/(-4)`

`x \leq -0.5`

From the list of given options, the correct answer is option C