SOLUTION: Solve for x, leave the solution on a number line and in interval notation 6x-5>but equal to 6/x

Algebra ->  Algebra  -> Rational-functions -> SOLUTION: Solve for x, leave the solution on a number line and in interval notation 6x-5>but equal to 6/x      Log On

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Question 349089: Solve for x, leave the solution on a number line and in interval notation
6x-5>but equal to 6/x
Answer by Fombitz(13828) About Me  (Show Source):
You can put this solution on YOUR website!
6x-5%3E=6%2Fx
Plot y=6x-5

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In addition now plot y=6%2Fx

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Find the intersection points, where 6x-5=6%2Fx
6x%5E2-5x=6
6x%5E2-5x-6=0
%283x%2B2%29%282x-3%29=0
Two solutions:
3x%2B2=0
3x=-2
x=-2%2F3
Then
y=6%28-2%2F3%29-5
y=-4-5
y=-9
(-2/3,-9)
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2x-3=0
2x=3
x=3%2F2
Then
y=6%2F%283%2F2%29
y=4
(3/2,4)
Plot those points.

Now look for the regions where the red line is above the green curve.
Solution region:(-2%2F3,0)U(3%2F2,infinity)