Question

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

Answer 1

Answer:

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.

Step-by-step 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.

Answer 2

Answer:

Solution is (-∞,∞)

Step-by-step 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 (-∞,∞)