SOLUTION: Thank you in advance for helping me with writing this problem in interval notation. t-1/t-5<=2

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
----------------------
t cannot be 1 as then the left side would be zero.
t cannot be 5 as then the left side would be undefined.
---------------
Solve the equality:
(t-1) = 2t-10
t = 9 (this is a piece of the solution)
--------------------------
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)
--------------------------------
Final solution: (-inf,1)U(1,5),[9,+inf)
================
Cheers,
Stan H.

RELATED QUESTIONS
Thank you in advance for helping me with this problem. (1/8)^-2t=2^t+3 (answered by jim_thompson5910)

Thank you in advance for helping me with writing this problem in interval notation. The... (answered by jim_thompson5910)

Thank you in advance for helping me with this problem: {{{ sqrt (p^2q^4)/ sqrt(pq) }}} (answered by ankor@dixie-net.com,Alan3354)

Hello I'm quite having a problem solving this since my teacher didn't teach it properly I (answered by josgarithmetic)

Could you please help me with this problem? Thank you in advance! Write sec t in terms (answered by Alan3354)

Thank you in advance for helping me with the following problems. I am struggling with... (answered by stanbon)

Thank you in advance for helping me with this problem. I need to find the (f o g)x and (answered by Fombitz)