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Which values from the set {-3, -2, 0, 2} satisfy this inequality?-x + 3 ≥ 3

User BTR
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1 Answer

7 votes

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.

User MuffinTheMan
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