Question 23316: Please help with this problem and its graph.
x-3/x+5 < 0
Thanks,
Marcus
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! Solving inequalities can most easily be solved by graphing calculator methods.
First of all, did you mean  or did you mean  ? I think you probably meant the first. I will solve this one, and if I have misinterpreted your problem, then either let me know by Email or re-post the problem and we'll give it another try.
The first step is to graph  . Because the problem says <0, you need to find all values of x for which the graph is BELOW THE X-AXIS! If the problem had been  , then you would draw the same graph, but to solve this one, you need to find all values of x where the graph of is ABOVE THE Y-AXIS!
So here is the graph:
Notice that the graph crosses the x-axis at x= 3. Notice that it looks like a vertical line at x=-5. This is actually an ASYMPTOTE, which SHOULD be drawn with a DOTTED LINE. An asymptote is a value of x where the graph will go off to infinity--it never quite gets to that value of x, which in this case is at x= -5. Notice that this graph is BELOW THE X-AXIS from -5 to 3, so the answer is  . Interval notation for this problem will be (-5,3).
This may not have been what you were expecting in a problem. I think it's MUCH easier than the old ways that I used to teach.
R^2 at SCC
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