Question 82827: i need someone to explain the steps to me in basic 'math for dummies' that my teacher is not able to do. the equation is:
x+4/x-4>_2 its one of those greater or equal to things. now, i am thinking that if i put the 2 on the other side with the equation and set it to >_0 then i can possibly graph it and get the places where it is zero on the graph. is this the way that it should be worked, am i close?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! x+4/x-4>_2
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1st: Take care of EQUALITY:
x+4 = 2x-8
x=12
Draw that as a vertical line thru all the points where x=12
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2nd: Take care of the INEQUALITY:
The fraction is zero if x=-4 so mark -4 on the x axis:
The fraction has a vertical asymptote at x=+4 so mark +4 on the x axis
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All that divides the x axis into 4 segments: (-inf,-4), (-4,4), (4,12), (12,+inf)
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Pick a test x value in each interval and check to see if it satisfies
the INEQUALITY. If it does the whole interval is part of the solution set.
If it does not that whold interval has no solutions.
Cheers,
Stan H.
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