SOLUTION: If 2/3 of a number, decreased by 1/2 is equal to 5/6, what is the number?

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Question 120202: If 2/3 of a number, decreased by 1/2 is equal to 5/6, what is the number?
Answer by solver91311(24713) About Me  (Show Source):
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Start with the number: x. Two-thirds of the number is 2x%2F3. Two-thirds of a number decreased by one-half is %282x%2F3%29-1%2F2. This expression is equal to 5%2F6, so we can write:

%282x%2F3%29-%281%2F2%29=5%2F6

The LCD of 2, 3, and 6 is 6, so:

%284x%2F6%29-%283%2F6%29=5%2F6

Add 3%2F6 to both sides:

4x%2F6=8%2F6

Multiply both sides by 6:

4x=8

Divide by 4:

x=2

Check:
%282%2F3%29%2A2=4%2F3. %284%2F3%29-%281%2F2%29=%288%2F6%29-%283%2F6%29=5%2F6, answer checks.