I need help with a question that I have missed. Here is my question
Solve the rational inequality. Write the answer in interval notation.
(3)/(x+1)>(-x)/(x+1)
Here is my answer in steps of how I solved it
(3)/(x+1)+(x)/(x+1)>0
(3(x+1)/(x+1)+(x(x+1)/(x+1)>0
(3x+3+x^2+x)/(x+1)>0
(x^2+4x+3)/(x+1)>0
(x+3)(x+1)/(x+1)>0
x+3=0
x=-3
x+1=0
x=-1
(-infinity,-5)
Sorry not sure what the infinity symbol is here on the forum
((-4+3)(-4+1))/(-4+1)>0
-1>0 False
(-3,-1)
((-2+3)(-2+1))/(-2+1)>0
1>0 True
(-1,infinity)
((0+3)(0+1))/(0+1)>0
3>0 True
So, I put my answer as (-3,-1)U(-1,infinity)
The correct answer was (-infinity,-3)U(-1,infinity)
The only thing I see that I done differently in the beginning was I moved the equation differently to equal it to zero. Here is how they moved the equation
0>(-x)/(x+1)-(3)/(x+1)
What did I do wrong? Do you move them in a certain direction or can you get the same answer no matter which end you have the zero on... if so how did I miss it?
Thanks,
Sunwers
Solve the rational inequality. Write the answer in interval notation.
(3)/(x+1)>(-x)/(x+1)
Here is my answer in steps of how I solved it
(3)/(x+1)+(x)/(x+1)>0
(3(x+1)/(x+1)+(x(x+1)/(x+1)>0
(3x+3+x^2+x)/(x+1)>0
(x^2+4x+3)/(x+1)>0
(x+3)(x+1)/(x+1)>0
x+3=0
x=-3
x+1=0
x=-1
(-infinity,-5)
Sorry not sure what the infinity symbol is here on the forum
((-4+3)(-4+1))/(-4+1)>0
-1>0 False
(-3,-1)
((-2+3)(-2+1))/(-2+1)>0
1>0 True
(-1,infinity)
((0+3)(0+1))/(0+1)>0
3>0 True
So, I put my answer as (-3,-1)U(-1,infinity)
The correct answer was (-infinity,-3)U(-1,infinity)
The only thing I see that I done differently in the beginning was I moved the equation differently to equal it to zero. Here is how they moved the equation
0>(-x)/(x+1)-(3)/(x+1)
What did I do wrong? Do you move them in a certain direction or can you get the same answer no matter which end you have the zero on... if so how did I miss it?
Thanks,
Sunwers
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