Question

Which of the following is the correct graph of the compound inequality 4p + 1 > −15 or 6p + 3 < 45?

Answer 1

Solution is (-∞,∞)

Explanation:

`4p + 1 > -15 \ or \ 6p + 3 < 45`

Solve each inequality separately

`4p + 1 > -15`

Subtract 1 from both sides

`4p> -16`

Divide both sides by 4

`p> -4`

Solve the second inequality

`6p + 3 < 45`

Subtract 3 from both sides

`6p< 42`

Divide both sides by 6

`p< 7`

`p> -4 \ or \p< 7`

Solution is (-∞,∞)

Answer 2

4p + 1 > −15 or 6p + 3 < 45

has solution any number.

The graph looks like this

<~~~~~~~~~~~~~~~~~~~~~~~~~~~>

---------(-4)---------(7)-------------

The shading is everywhere from left to right.

Explanation:

Let's solve this first:

4p+1>-15

Subtract 1 on both sides:

4p>-16

Divide both sides by 4:

p>-4

or

6p+3<45

Subtract 3 on both sides:

6p<42

Divide both sides by 6:

p<7

So our solution is p>-4 or p<7

So let's graph that

~~~~~~~~~~~~~~~~~~~~~~~~~~~~O

O~~~~~~~~~~~~~~~~~~~~~~~~~~~~ p>-4

---------------------(-4)---------------------(7)--------------------

or is a key word! or means wherever the shading exist for either is a solution.

So this shading is everywhere.

The answer is all real numbers.

The final graph looks like this:

<~~~~~~~~~~~~~~~~~~~~~~~~~~~>

---------(-4)---------(7)-------------

The shading is everywhere from left to right.