Question

Which of the following is the correct graph of the compound inequality 4p + 1 > −7 and 6p + 3 < 33

Answer 1

p lies between  - 2  & 5

Step-by-step explanation:

4p + 1 > −7

subtracting 1 from both sides

=> 4p > -8

Dividing by 4 both sides

=> p > - 2

6p + 3 < 33

subtracting 3 from both sides

=> 6p < 30

Dividing by 6 both sides

=> p  < 5

 -2 < p  < 5

p lies between  - 2  & 5

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Answer 2

The solution for the compound inequality is $-2 < p <5$

Step-by-step explanation:

Consider the provided inequality.

$4p + 1> -7$

Subtract 1 from both sides

$4p> -8$

Divide both sides by 4.

$p> -2$

So the value of p should be greater than -2.

Consider the second inequality.

$6p + 3 < 33$

Simplify as shown below:

$6p<30$

$p < 5$

The value of p should be less than 5.

Hence, the solution for the compound inequality is $-2 < p <5$

In interval notation $p\in (-2,5)$

The required graph is shown below:

The open dot shows that -2 and 5 is not included in the solution set.

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