Question

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

Answer 1

x ≤ -1/2

Explanation:

2x – 6 ≥ 6(x – 2) + 8

Solve the inequality and then we graph it on number line

2x – 6 ≥ 6(x – 2) + 8 (distribute 6 inside the parenthesis)

2x – 6 ≥ 6x – 12 + 8

2x – 6 ≥ 6x – 4

Subtract 6x from both sides

-4x - 6 ≥ -4

Add 6 on both sides

-4x ≥ 2

Divide both sides by -4

x ≤ -1/2

Now we make a number line

put closed circle at -1/2 and shade to the left

Answer 2

The solution to the given expression is shown below:
2X - 6 ≥ 6(X-2) +8

Remove parenthesis by performing multiplication:
2X - 6 ≥ 6X - 12 +8

Transpose and combine the same term:
-6 + 12 -8 ≥ 6X -2X
-2 ≥ 4X

Perform division:
-2/4 ≥ x