SOLUTION: (3x-4)/x<=(-2) The answer appears to be x<=4/5 but how do you prove that x must also greater than 0?

Algebra ->  Inequalities -> SOLUTION: (3x-4)/x<=(-2) The answer appears to be x<=4/5 but how do you prove that x must also greater than 0?      Log On


   

Question 133651: (3x-4)/x<=(-2)
The answer appears to be x<=4/5 but how do you prove that x must also greater than 0?
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
(3x-4)/x<=-2
x(3x-4)/x<=-2x
3x-4<=-2x
3x+2x-4+4<=-2x+2x+4
5x<=4
5x/5=4/5
x<=4/5
x cannot be 0 because in the original equation there would be division by 0 which is not allowed. x cannot be less than 0 because, as you can see from the graph below y>0 when x<0
So, X(0, 4/5]
or 0 .
Ed
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graph%28500%2C500%2C-2%2C2%2C-10%2C10%2C%283x-4%29%2Fx%29