(4-x)/2 is greater than or equal to (2-x)/3?

To solve this inequality, we can first simplify both sides:

(4-x)/2 ≥ (2-x)/3

Multiplying both sides by 6 to get rid of the denominators:

3(4-x) ≥ 2(2-x)

Expanding both sides:

12 - 3x ≥ 4 - 2x

Now, we can simplify and solve for x:

12 - 3x ≥ 4 - 2x
12 - 4 ≥ 3x - 2x
8 ≥ x

Therefore, the solution to the inequality is x ≤ 8.

Multiply both sides by 6 to clear the fraction.

3(4-x) ≥ 2(2-x)
12-3x ≥ 4-2x
12-4 ≥ -3x+2x
8 ≥ -x
-8 ≤ x

Therefore, the solution set is (-∞, -8].