SOLUTION: I sent this problem earlier but after receiving a response quickly realized I entered the wrong problem, can u please help me with this one? I have no clue where to start. Thanks i

Question 242760: I sent this problem earlier but after receiving a response quickly realized I entered the wrong problem, can u please help me with this one? I have no clue where to start. Thanks in advance!!
Solve:
(x+2)(x-2)(x+1)>0
a)the solution set is
b)solution is all real numbers
c)there is no solution
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given inequality.

Set the left side equal to zero

Set each individual factor equal to zero:

, or

Solve for x in each case:

, or

So our critical values are , and

Now set up a number line and plot the critical values on the number line

So let's pick some test points that are near the critical values and evaluate them.

Let's pick a test value that is less than (notice how it's to the left of the leftmost endpoint). This corresponds to the left most interval ()

So let's pick

Start with the given inequality

Plug in

Evaluate and simplify the left side

Since the inequality is false, this means that the interval does not work. So this interval is not in our solution set and we can ignore it.

---------------------------------------------------------------------------------------------

Let's pick a test value that is in between and . This corresponds to the left middle interval ()

So let's pick

Start with the given inequality

Plug in

Evaluate and simplify the left side

Since the inequality is true, this means that the interval works. So this tells us that this interval is in our solution set.
So part our solution in interval notation is ()

---------------------------------------------------------------------------------------------

Let's pick a test value that is in between and . This corresponds to the right middle interval ()

So let's pick

Start with the given inequality

Plug in

Evaluate and simplify the left side

Since the inequality is false, this means that the interval does not work. So this interval is not in our solution set and we can ignore it.

---------------------------------------------------------------------------------------------

Let's pick a test value that is greater than (notice how it's to the right of the rightmost endpoint). This corresponds to the right most interval ()

So let's pick

Start with the given inequality

Plug in

Evaluate and simplify the left side

Since the inequality is true, this means that the interval works. So this tells us that this interval is in our solution set.
So part our solution in interval notation is ()

---------------------------------------------------------------------------------------------

Summary:

So the solution in interval notation is:

() ()

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

First thing to do is to solve the problem that you posted before, namely:

Take the three roots of this equation, call them , , and (in ascending numerical order) and create four intervals.

For each of the four intervals, select a value and substitute it back into the original inequality. Once you have done that, two of the values will result in true statements and two of them will make the original inequality false. The union of the two intervals from which the values that made the original inequality true is the solution set of your inequality.

John

RELATED QUESTIONS
I asked for help with this problem earlier but I entered it wrong. Rationalize the... (answered by Alan3354)
I sent a problem yesterday and didn't get a response so can somebody please help me step... (answered by addingup)
hi!m i need hel in this problem and Im wonderinr if you can hel me....... (answered by jim_thompson5910)
Could you please help me to solve this problem.The problem -If one zero of a polynomial... (answered by sudhanshu_kmr)
Hello, I tried solving this problem, but my answer of $2880 was labelled wrong. Here... (answered by solver91311)
Will you please hel pme with this problem? I tried really hard on it ans it was counted... (answered by checkley75)
Will you please hel pme with this problem? I tried really hard on it ans it was counted... (answered by stanbon)
I'm so sorry. I just sent you a question and gave you the wrong email address. I am a... (answered by MathLover1)
hi have to resolve this problem but i have trouble to answer can u help me the problem... (answered by Boreal)