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Which of the following points is not a solution of the inequality y ≥ |x| + 3?

(-3, 6)
(0, 4)
(-3, 0)

1 Answer

4 votes

Answer: Choice C

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Step-by-step explanation:

If we plug the coordinates of point A into the inequality, then we get

y ≥ |x| + 3

6 ≥ |-3| + 3

6 ≥ 3 + 3

6 ≥ 6

Which is true. Since we're looking for a non-solution, we rule out choice A.

You should find choice B is a similar story to choice A, so we can rule this out as well.

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Choice C is the answer because

y ≥ |x| + 3

0 ≥ |-3| + 3

0 ≥ 3 + 3

0 ≥ 6

which is false.

Check out the graph below and notice how point C is not in the shaded solution region, and it's not on the boundary either. This is a visual way to quickly find the answer.

The boundary line y = |x|+3 is solid because of the "or equal to". We shade above the boundary line due to the greater than sign.

Which of the following points is not a solution of the inequality y ≥ |x| + 3? (-3, 6) (0, 4) (-3, 0)-example-1
User Tapan Nallan
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