SOLUTION: could you please help me solve this equation x-1 >(or equal) 6/x I tried and received [-2,0) U [3,infinity) but I am not certain if that is correct

Algebra ->  Inequalities -> SOLUTION: could you please help me solve this equation x-1 >(or equal) 6/x I tried and received [-2,0) U [3,infinity) but I am not certain if that is correct      Log On


   

Question 1093771: could you please help me solve this equation
x-1 >(or equal) 6/x
I tried and received [-2,0) U [3,infinity) but I am not certain if that is correct
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x-1 >(or equal) 6/x

x-1>=6/x
x-1%3E=6%2Fx


x-1-6%2Fx%3E=0
%28x%2Fx%29x-x%2Fx-6%2Fx%3E=0
%28x%5E2-x-6%29%2Fx%3E=0
which looks like an inequality already solved on this site, recently;

%28%28x-3%29%28x%2B2%29%29%2Fx%3E=0--------critical x values are -2, 0, 3.

INTERVALS TO CHECK 
            (-infin, -2]         [-2, 0)           (0,3]           [3, infin)

sign        (-)(-)/(-)=-        (-)(+)/(-)=+      (-)(+)/(+)=-     (+)(+)/(+)=+
value      FALSE                TRUE              FALSE            TRUE

The solution set will be all the intervals which make the inequality true.
This is [-2,0) AND [3,infinity).
(The intervals should really be checked using the original inequality).

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
could you please help me solve this equation
x-1 >(or equal) 6/x
I tried and received [-2,0) U [3,infinity) but I am not certain if that is correct
Yes, you're perfectly correct. Good job!

ABSOLUTELY NOTHING else needs to be said or done!