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

Solution:

Given: Inequality is 2x - 6 ≥ 6(x - 2) + 8

Solving for the variable x while retaining the inequality sign we have

2x - 6 ≥ 6x - 12 + 8

Rearrangement leads to

-6 + 12 - 8 ≥ 6x - 2x

- 2 ≥ 4x

-1/2 ≥ x

The inequality could be represented on the number line as follows:

It should be noted that when the inequality includes the equal to sign i.e. ≤ then the dot symbol is dark as shown on the number line i.e. ⚫. If the inequality sign does not include equal to sign then the dot is blank ⚪.

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

Summary:

The inequality 2x - 6 ≥ 6(x - 2) + 8 which is represented by the number line above shows that the variable x takes on values that lie on the left-hand side of the number line value x = -1/2 and includes the point x = -1/2.