SOLUTION: Solve the following 3x-3/x+1<_ 2

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Question 665383: Solve the following 3x-3/x+1<_ 2
Found 2 solutions by lynnlo, stanbon:
Answer by lynnlo(4176) About Me  (Show Source):
You can put this solution on YOUR website!
PROBLEM:
3X-3/X+1≤2
=X≤1-√37/6
OR
0

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(3x-3)/(x+1) <= 2
------------
Factor:
[3(x-1)/(x+1)] <= 2
------------
x cannot be -1
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Solve the Equality:
(3x-3)/(x+1) = 2
3x-3 = 2x+2
x = 5
--------
Draw a number line and plot x = -1, x = 5
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Test the interval (-oo,-1)
[3(x-1)/(x+1)] <= 2
If x = -3 you get (3(-4))/(-2) = 6 < 2 False
so no solutions where -oo ------------------------------------
Test -1< x <5:
[3(x-1)/(x+1)] <= 2
If x = 0 you get (3(-1))/(1) = -3 <=2 True,
so solution in the interval (-1,5]
------------------------------------
Test the interval (5,+oo)
[3(x-1)/(x+1)] <= 2
If x = 10 you get (3(9))/(11 = 27/11 = 2 5/11 <= 2 False,
so no solutions in (5,+oo)
================================
Cheers,
Stan H.