SOLUTION: Solve the inequality {{{(3-x)/(x-4)>=2}}}

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Question 705583: Solve the inequality
%283-x%29%2F%28x-4%29%3E=2
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
What you really want to ask about is the adjusted inequality.

%283-x%29%2F%28x-4%29%3E=2

If x-4 is positive, then %283-x%29%3E=2%28x-4%29
3-x>=2x-8
3+8>=3x
11>=3x
11/3>=x

If x-4 is negative, then %283-x%29%3E=2%284-x%29. Check that carefully to understand before continuing.
3-x>=8-2x
3-8-x>=-2x
3-8>=-2x+x
-5>=-x
5<=x [(watch what that says carefully].

x%3C=11%2F3 OR x%3E=5