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!
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I think the answer is (-infinity, -11/3] U (8,0) ??? I'm confused on the second part. Thank you!
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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):
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
