Question 149692This question is from textbook
: Thank you in advance for helping me with writing this problem in interval notation. t-1/t-5<=2
This question is from textbook
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! (t-1)/(t-5) <= 2
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t cannot be 1 as then the left side would be zero.
t cannot be 5 as then the left side would be undefined.
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Solve the equality:
(t-1) = 2t-10
t = 9 (this is a piece of the solution)
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Draw a number line and mark t = 1, t = 5 and t = 9.
Now check a test point from each of the resulting number-line intervals
to see where the solutions are:
Checking t=0 you get (0-1)/(0-5) < 2 ; true, so solutions in (-inf,1)
Checking t=2 you get (2-1)/(2-5) < 2 : true, so solutions in (1,5)
Checking t=8 you get(8-1)/(8-5) < 2; false, so no solutions in (5,9)
Checking t=10 you get (10-1)/(10-5) < 2; true, so solutions in [9,+inf)
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Final solution: (-inf,1)U(1,5),[9,+inf)
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Cheers,
Stan H.
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