Question 814095: Hello, I'm trying to help my son with a community college math problem. Here is the question on his homework. Please help us!
We have found, in the first equation that x= - 1. We are at a loss as to what the other two equations mean and need?
Appreciate any and all help.
Kymberly
Found 2 solutions by josgarithmetic, Edwin McCravy:
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! What is the exact problem description? What is given as known? What is the question, exactly? A tutor must be able to know all the details of your exercise if any help is to be given.
Answer by Edwin McCravy(20055)  (Show Source):
You can put this solution on YOUR website! Hello, I'm trying to help my son with a community college math problem. Here is the question on his homework. Please help us!
 > or= to 0
The critical numbers are numbers that cause
the expression to be 0 or undefined. x=-1
causes the numerator to be 0, so -1 is one
critical number x=4 causes the denominator
to become 0, and the expression to be
undefined. So 4 is the other critical number.
Place the critical numbers on a number line:
---------o--------------o--------------
-1 4
That divides the real number into
three regions and two critical values.
(-oo,-1), {-1}, (-1,4), {1}, (1,oo}
choose a convenient point in (-oo,-1)
Substitute in -2
 > or = to 0
 > or= to 0
 > or= to 0
That is true so we shade (-oo,-1)
<========○--------------○-----------
-1 4
Next we test the critical value -1
(x+1)/(x-4) > or= to 0
(-1+1)/(-1-4) > or= to 0
0 > or= to 0
So we darken the circle at -1,
and so the solution set contains
(-oo,-1]
<========●--------------o--------------
-1 4
choose a convenient point in (-1,4)
Substitute in 0
> or = to 0
 > or= to 0
 > or= to 0
That is false so we do not shade
(-1,4)
Next we test the critical value 4
(x+1)/(x-4) > or= to 0
(4+1)/(4-4) > or= to 0
5/0 > or= to 0
That is undefined so we no not darken
the circle at 4.
<========●--------------o--------------
-1 4
choose a convenient point in (4,oo)
Substitute in 5
> or = to 0
 > or= to 0
 > or= to 0
That is true so we shade (4,oo)
<========●--------------o=============>
-1 4
So the solution is
(-oo,-1] U (4,oo)
You do the other one.
Edwin
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