# Which of the following is the correct graph of the compound inequality 4p + 1 > −7 or 6p + 3 <

###### Question:

a: a number line with open circles at negative 2 and 5 with shading in between.

b: number line with open dot at negative 2 with shading to the left and an open dot at 5 with shading to the right

c: number line with shading everywhere.

d: number line with open dot at negative 2 and a closed dot at 5 with shading in between

## Answers

1) 4p + 1 > - 7 => 4p > - 8=> p > - 2graph: < || -4 -3 -2 2) 6p + 3 < 33=> 6p < 33 - 3=> 6p < 30=> p < 5graph: < -2 -1 0 1 2 3 4 5compounded graph: < -2 -1 0 1 2 3 4 5

4p + 1 > -7 6p + 3 < 33

4p > -7 - 1 6p < 33 - 3

4p > -8 6p < 30

p > -8/4 p < 30/6

p > -2 p < 5

p > -2 or p < 5 It will have a open circle on -2, with shading to the right...and a open circle on 5, with shading to the left...or basically, open circles on -2 and 5, with shading in between

5p+7p

Step-by-step explanation:

Answer with explanation:

The two compound Inequality is

1. →→4 p +1 > -7

Subtracting , 1 from both sides

→4 p +1 -1 > -7 -1

→ 4 p > -8

Dividing both sides by, 4 we get

p > -2

⇒⇒Second , Inequality is

6 p + 3 < 33

Subtracting , 3 from both sides

→6 p +3 - 3 < 33 -3

→6 p < 30

Dividing both sides by 5, we get

→p<5

The solution of the two combined inequality is

1.→ p > -2 and p < 5.

≡-2 < p <5

Combining them we get the solution set,which is, p ∈ (-2,5)

Option A: →A number line with open circles at negative 2 and 5 with shading in between.

[tex]Me which of the following is the correct graph of the compound inequality 4p + 1 > −7 or[/tex]

Option: A is the correct answer.

A. a number line with open circles at -2 and 5 with shading in between.

Step-by-step explanation:We are given a system of linear inequality in terms of variable ''p'' as:

(1) [tex]4p+1-7[/tex]

on subtracting -1 from both side of the inequality we get:

[tex]4p-8[/tex]

Now on dividing both side of the inequality by 4 we get:

[tex]p-2[/tex]

Hence, the region that is obtained is:

(-2,∞)

(2) [tex]6p+3<33[/tex]

on subtracting -3 from both side of the inequality we get:

[tex]6p<30[/tex]

Now on dividing both side of the inequality by 5 we get:

[tex]p<5[/tex]

Hence, the region that is obtained is:

(-∞,5)

Hence, the common region that is obtained by both the inequalities is:

(-2,5)

i.e. the graph will be a number line with open circle both at -2 and 5 and shading in between them.

[tex]Which of the following is the correct graph of the compound inequality 4p + 1 > −7 or 6p + 3 <[/tex]

set of all real numbers (-∞,∞)

Step-by-step explanation:

Solve each inequality

[tex]4p+1-7[/tex]

Subtract 1 from both sides

[tex]4p-8[/tex]

Divide by 4 on both sides

[tex]p-2[/tex]

[tex]6p+3 <33[/tex]

Subtract 3 from both sides

[tex]6p<30[/tex]

Divide both sides by 6

[tex]p<5[/tex]

[tex]p-2[/tex] or [tex]p<5[/tex]

The graph is attached below

[tex]Which of the following is the correct graph of the compound inequality 4p+1> -7 or 6p+3 < 33?[/tex]

Step-by-step explanation:

4p+1>-7 , p>-2

6p+3<33 , p<5

-2<p<5

[tex]Which of the following is the correct graph of the compound inequality 4p+1>-7 or 6p+3<33 ( t[/tex]

The answer is B :)

I hope this helped

The answer is B

I hope this helped :)

We are given compound inequality 4p + 1 > −7 or 6p + 3 < 33.

Let us solve each of the inequality one by one.

4p + 1 > −7

Subtracting 1 from both sides, we get

4p + 1-1 > -7-1

4p > -8

Dividing both sides by 4, we get

p > -2. (Shading right side for greater than sign)

Solving 6p + 3 < 33.

Subtracting 3 from both sides, we get

6p + 3-3 < 33-3.

6p < 30

Dividing both sides by 6, we get

p < 5. (Shading left for less than sign)

We have less than and greater than symbols in both inequalities, therefore we would have open circles(dots) on -2 and 5.

And because we have "OR" composite inequality.

So, we would take the combination of both shaded portion.

Therefore, correct option is C.number line with shading everywhere..