Question 1007206: Solve the following inequality using interval notation:
1/x+3 + 1/x >_ 0
>_ = greater than or equal to
PLEASE HELP
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! x can't be 0 or -3
Multiply through by x(x+3) to clear fractions, and you get x+x+3>=0, 2x+3>=0 and x>=-3/2.
critical values are <-3, between -3 and -3/2, between -3/2 and 0, and greater than 0.
pick -4
-1+-1/4 is not greater than or equal to zero.
pick -2
1-1/2 not greater than or equal to zero. That works.
Pick -3/2 itself. 1/1.5-1/(-3/2)=2/3-2/3 =0. That works.
Try -1
1/2 -1 is not greater than 0.
>0, both are positive and it works.
The inequality works
(-3,-3/2]U[0,oo)
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