PLEASE HELP ME  Which of the following is the correct graph of the compound inequality 4p + 1 > −7 or 6p + 3 < 33? (1 poin

Response with explanation:

We have two compound inequalities to consider:

1. →→4 p + 1 > -7

By subtracting 1 from both sides, we obtain:

→4 p + 1 - 1 > -7 - 1

→ 4 p > -8

When we divide both sides by 4, it leads us to

p > -2

Then, for the second inequality:

6 p + 3 < 33

By subtracting 3 from both sides, we have:

→6 p + 3 - 3 < 33 - 3

→6 p < 30

Dividing both sides by 5 yields:

→p < 5

Consequently, the combined solution of the two inequalities is:

1.→ p > -2 and p < 5.

≡-2 < p < 5

By combining, our solution set is reflected as p ∈ (-2,5).

Option A corresponds to: →A number line with open circles at -2 and 5, shaded in between.

For the first inequality, the solution is derived as follows:
4p > -8...... by subtracting 1
p > -2....... when divided by 4
This solution is represented on a graph as an open dot at -2, with the shading extending rightwards.

Since no inequality symbols incorporate "or equal to", all depicted dots remain open. The correct option is the first one:
a number line marked with open circles at -2 and 5, shaded in between.