Question 365282: Solve the inequality, state the solution using the interval notation and graph.
x - 3 < 0
_____
x + 5
Found 2 solutions by stanbon, jokaehler:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Solve the inequality, state the solution using the interval notation and graph.
x - 3 < 0
_____
x + 5
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Find the boundary values.
x = 3 because the numerator cannot be zero.
x = -5 because the denominator cannot be zero.
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Draw a number line and plot those two values.
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Check a value in each resulting interval in the
INEQUALITY to see where the solutions are.
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(x-3)/(x+5) < 0
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If x = -10 you get -/- < 0; false
If x = 0 you get -/+ < 0; true, so solutions in (-5,3)
If x = 10 you get +/+ <0; false
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Solution: (-5,3)
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Cheers,
Stan H.
Answer by jokaehler(26)  (Show Source):
You can put this solution on YOUR website! In order to figure out what this graph looks like, we need to find vertical and horizontal asymtotes. Asymtotes are a part of a graph of which it is impossible to get the number.
Vertical Asymtotes: In order to find vertical asymtotes, we need to set the denominator to zero so that we get a "div by 0" error on our calculator if we were to calculate it. To solve for this one (x+5), we need to get it so that it equals 0.
Horizontal Asymtotes: In order to find horizontal asymtotes, we need to look at the degrees of the fraction. On the numerator, the degree is 1 (x-3). On the denominator, the degree is also 1 (x+5). We divide the two degrees (1/1) and that is our horizontal asymtote.
Now that we have found the asymtotes, we can now find the domain.
The domain goes from negative infinity to -5, and then goes to -5 to infinity.
The horizontal asymtote does not affect the domain; it affects the range.
Answer:
(-infinity, -5)U(-5, infinity)
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