Question

Which inequality matches the graph?

Answer 1

The fourth option is the correct one

-5p+4> 14
-5p>10
-p>2

Answer 2

The graph shows p > 2. There is no line under the "greater than" sign since we want to exclude the endpoint p = 2. This is what the open hole indicates.

Solve each of the answer choices to see which leads to p > 2

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Choice A
5p+4 > 14
5p+4-4 > 14-4
5p > 10
5p/5 > 10/5
p > 2

So we found the answer on the first try. 

Let's check the others
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Choice B

This will follow the same exact steps as choice A above, but instead we'll have an underline under each "greater than" sign. As explained above, there is no underline. So we can rule out choice B.
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Choice C

5p-4 > 14
5p-4+4 > 14+4
5p > 18
5p/5 > 18/5
p > 3.6

We can eliminate choice C
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Choice D

-5p+4 > 14
-5p+4-4 > 14-4
-5p > 10
-5p/(-5) < 10/(-5) ... inequality sign flips
p < -2 

We can eliminate choice D
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So the only answer is choice A