SOLUTION: Professor I need help with this problem. 3y+11/y-8 ≤ 0 I think the answer is (-infinity, -11/3] U (8,0) ??? I'm confused on the second part. Thank you!

Question 650342: Professor I need help with this problem. 3y+11/y-8 ≤ 0
I think the answer is (-infinity, -11/3] U (8,0) ??? I'm confused on the second part. Thank you!
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

If you have a rational expression of the form

then

and

must be of opposite signs. If they were the same sign, then you would have a positive value for the rational expression which would make the relation false.

Therefore we either have

and

Note that we must not allow the denominator to equal zero.

Solving these two inequalities gives:

AND

Which is absurd --

cannot simultaneously be larger than 8 and smaller than a number in the vicinity of -4.

Try it the other way:

and

Again, we must not allow the denominator to equal zero.

Solving these two inequalities gives:

AND

Which gives the solution set:

John

My calculator said it, I believe it, that settles it

The Out Campaign: Scarlet Letter of Atheism

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SOLUTION: Professor I need help with this problem. 3y+11/y-8 &#8804; 0 I think the answer is (-infinity, -11/3] U (8,0) ??? I'm confused on the second part. Thank you!

SOLUTION: Professor I need help with this problem. 3y+11/y-8 ≤ 0 I think the answer is (-infinity, -11/3] U (8,0) ??? I'm confused on the second part. Thank you!