Which ordered pair is not a solution of the inequality, 3x − 2y ≥ 12

a.
(-3, -10.5)

b.
(-1, -7)

c.
(0, -6)

d.
(2, -3)

Let's go through the answer choices one by one

Choice A

Plug in (x,y) = (-3, -10.5)
3x - 2y >= 12
3(-3) - 2(-10.5) >= 12
-9 + 21 >= 12
12 >= 12

The last inequality is true, so the first inequality is true when (x,y) = (-3, -10.5)

Therefore, (-3,-10.5) is a solution
We can eliminate choice A because we are looking for non-solutions.
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Choice B

Plug in (x,y) = (-1, -7)
3x - 2y >= 12
3(-1) - 2(-7) >= 12
-3  + 14 >= 12
11 >= 12

The last inequality is false, so the first inequality is false when (x,y) = (-1, -7)

Therefore, (-1,-7) is NOT a solution

The answer must be choice B since we're looking for non-solutions. Let's see what choice C and choice D have to say. 

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Choice C

Plug in (x,y) = (0, -6)
3x - 2y >= 12
3(0) - 2(-6) >= 12
0 + 12 >= 12
12 >= 12

The last inequality is true, so the first inequality is true when (x,y) = (0, -6)

Therefore, (0, -6) is a solution
We can eliminate choice C because we are looking for non-solutions.

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Choice D

Plug in (x,y) = (2, -3)
3x - 2y >= 12
3(2) - 2(-3) >= 12
6 + 6 >= 12
12 >= 12

The last inequality is true, so the first inequality is true when (x,y) = (2, -3)

Therefore, (2, -3) is a solution
We can eliminate choice D because we are looking for non-solutions.

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In summary, the final answer is choice B.

If you look at the attached graph, you'll notice that only point B is not in the shaded region (which represents the solution set). Any points on the boundary count as part of the solution. 

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