Question

which number line represents the solution set for the inequality $2x - 6 \geq 6(x - 2) + 8$? \
(four number line options are shown, with markings at -1.5, -1, -0.5, 0, 0.5, 1, 1.5 and different blue line segments and arrow directions)

Explanation:

Step1: Expand right-hand side

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

Step2: Simplify right-hand side

$2x - 6 \geq 6x - 4$

Step3: Move x terms to left

$2x - 6x - 6 \geq -4$

Step4: Simplify x terms

$-4x - 6 \geq -4$

Step5: Move constant to right

$-4x \geq -4 + 6$

Step6: Simplify right-hand side

$-4x \geq 2$

Step7: Divide by -4 (reverse inequality)

$x \leq \frac{2}{-4}$
$x \leq -0.5$

Answer:

The number line with a closed dot at -0.5 and an arrow pointing left (the third option from the top)