SOLUTION: Solve: (x+16)/(x-2)<=7

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Question 846031: Solve: (x+16)/(x-2)<=7
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Subtract 7 from both sides.
%28x%2B16%29%2F%28x-2%29-7%28%28x-2%29%2F%28x-2%29%29%3C=0
%28x%2B16-7x%2B14%29%2F%28x-2%29%3C=0
%28-6x%2B30%29%2F%28x-2%29%3C=0
Look at the zeros of the numerator and the undefined values of the denominator and break up the number line.
x=5
x=2
Test for values less than 2, between 2 and 5, and greater than 5.
First, less than 2, x=0,30%2F%28-2%29%3C=0, -15%3C=0, True.
Between 2 and 5, x=3, %28-18%2B30%29%2F%283-2%29%3C=0,12%3C=0, False.
Greater than or equal to 5, x=6, %28-6%286%29%2B30%29%2F%286-2%29%3C=0,-6%2F3%3C=0,-2%3C=0, True.
So the solution set is,
(-infinity,2)U[5,infinity)