SOLUTION: solve x^2-6x>-8 and 1/(t-5)<3/(t+5) Thanks!

Question 66526: solve
x^2-6x>-8
and
1/(t-5)<3/(t+5)
Thanks!
Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
x^2 - 6x > -8
x^2 - 6x + 8 > 0
x^2 - 4x - 2x + 8 > 0
(x^2 - 4x) + (-2x + 8) > 0
x(x - 4) - 2(x - 4) > 0
(x - 2)(x - 4) > 0
<========(2)---------(4)=========>
and
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1/(t - 5) < 3/(t + 5)
(t^2 - 25)/(t - 5) < 3(t^2 - 25)/(t + 5)
t + 5 < 3(t - 5)
t + 5 < 3t - 15
20 < 2t
10 < t

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