Question

which of the following is the correct graph of the compound inequality 4p + 1> -7 and 6p + 3 < 33 ?

Answer 1

Answer:  Choice C

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Explanation:

Let's solve the first inequality for p

4p+1 > -7

4p > -7-1

4p > -8

p > -8/4

p > -2

And we'll do the same for the second inequality as well

6p+3 < 33

6p < 33-3

6p < 30

p < 30/6

p < 5

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We've found that p > -2 and p < 5

This must mean -2 < p < 5

The graph of which consists of open holes at -2 and 5 on the number line, then we shade in between those open holes. The open holes are to indicate "do not include the endpoint as part of the shaded solution set".

We can say that p is between -2 and 5, excluding both endpoints.

So that's why graph C is the final answer.