SOLUTION: I have the following problem, not positive that I've figured it right. Could someone help me please. Thank you. When the reciprocal of three times a number is subtracted from the r

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Question 130187: I have the following problem, not positive that I've figured it right. Could someone help me please. Thank you. When the reciprocal of three times a number is subtracted from the reciprocal of the number, the result is one-sixth. Find the number. I came up with x+3x-x=1/6 x=1/18 Is this correct? Thank you for your help.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
No intention to damage your self-esteem here, but you are not even close.

The reciprocal of a number is just 1 divided by that number. So if x is your number, the reciprocal is 1%2Fx.

You are asked to take the reciprocal of 3 times a number: 1%2F3x and subtract that from the reciprocal of the number, so:

%281%2Fx%29-%281%2F3x%29

And this is equal to one-sixth, so:

%281%2Fx%29-%281%2F3x%29=1%2F6

The common denominator is 3x, so:

%283-1%29%2F3x=1%2F6

2%2F3x=1%2F6

3x=12

x+=+4

Check the answer:

1%2F4-1%2F12=3%2F12-1%2F12=2%2F12=1%2F6 Answer checks.