Answer: -3, -2, 0
Step-by-step explanation
Let's isolate x.
-x+3 ≥ 3
-x ≥ 3-3
-x ≥ 0
x ≤ 0/(-1)
x ≤ 0
Take note when dividing both sides by a negative number, the inequality sign flips. Of the values {-3,-2,0,2}, only {-3,-2,0} form the solution set.
For example, if x = -3 then,
-x+3 ≥ 3
-(-3)+3 ≥ 3
3+3 ≥ 3
6 ≥ 3
We arrive at a true statement, which makes -x+3 ≥ 3 true when x = -3.
Similar true statements happen when x = -2 and x = 0.
In contrast, x = 2 is not a solution because of this scratch work.
-x+3 ≥ 3
-2+3 ≥ 3
1 ≥ 3
The last inequality is false, so the original inequality is false when x = 2. This is why x = 2 is not in the solution set.
The graph of x ≤ 0 will have a closed filled in circle at x = 0 on the number line. Then we shade to the left. This visually indicates all values equal to 0 or smaller than 0.