Question

Which number line represents the solution set for the inequality 2x - 6 2 6(x - 2) + 8?-1.5-1-0.500.51.5-1.5-1-0.500.51.55-0.500.51.5-1-0.500.51.5

Answer 1

Solve the inequality:

2x - 6 ≥ 6(x - 2) + 8

Operating the parentheses:

2x - 6 ≥ 6x - 12 + 8

Subtracting 6x:

2x - 6x - 6 ≥ - 12 + 8

Adding 6:

2x - 6x ≥ - 12 + 8 + 6

Simplifying:

- 4x ≥ 2

Dividing by -4 and changing the symbol:

x ≤ 2/(-4)

x ≤ -0.5

The solution in the number line starts at -0.5 and goes to the left with an arrow: