SOLUTION: Solve and give answer in interval notation {{{(4x-5)/(x+3)<3}}}

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Question 135440: Solve and give answer in interval notation

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Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First, let's find the vertical asymptote

x%2B3=0 Set the denominator equal to 0


x=-3 Solve for x


So the vertical asymptote is x=-3. If we graph, we can see that the vertical asymptote is a critical value. So from the graph, we can see that anything to the left of x=-3 is not in the interval. So this means that one part of the solution is x%3E-3



+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+%284x-5%29%2F%28x%2B3%29%29+


Start with the given inequality


Multiply both sides by x%2B3


Distribute


Subtract 3x from both sides


Add 5 to both sides



So another part of the solution is x%3C14


Answer:

So the answer in interval notation is