# Naive set theory - show two sets are equal

• November 8th 2010, 11:09 AM
MattWT
Naive set theory - show two sets are equal
Hi,

Suppose two sets:

C = {x member of real numbers | x doesnot euqal 2 and {6x+1}/{x-2} < or equal 1

D = [-{3}/{5}, 2)

How would I begin this?

I've tried rearranging the equation in C, to give, x < equal -3/5, which is wrong

I've also randomly plugged in numbers less than 1 into the equation, such as -5, which gives 4.1.... which isn't in the set.

Quite confused here

Thanks!
• November 8th 2010, 11:13 AM
Plato
Can you solve the inequality $\dfrac{6x+1}{x-2}\le1~?$
• November 9th 2010, 03:55 AM
HallsofIvy
No need to solve that inequality for this problem! D only has two members, -3/5 and 2, and the definition of C specifically says "x is not equal to 2". What does that tell you?
• November 9th 2010, 04:21 AM
Plato
Quote:

Originally Posted by HallsofIvy
No need to solve that inequality for this problem! D only has two members, -3/5 and 2, and the definition of C specifically says "x is not equal to 2". What does that tell you?

I think you misread the notation. I read it as $D = \left[ {\frac{{ - 3}}{5},2} \right)$
• November 10th 2010, 03:48 AM
HallsofIvy
You are right. Too bleary eyed, I suspect. Thanks.