To solve the equation 1/3 - 5/6 = 1/X, we want to get rid of the fractions by finding a common denominator and then multiplying both sides of the equation by that common denominator.
First, let's find the common denominator for 1/3 and 5/6. The least common multiple (LCM) of 3 and 6 is 6. So we can rewrite the equation as (6/6) * (1/3) - (6/6) * (5/6) = (6/6) * (1/X).
Simplifying each term, we get (6/18) - (30/36) = 6/X.
Now, let's clear the fractions by multiplying through by 36X:
36X * (6/18) - 36X * (30/36) = 36X * (6/X).
Simplifying further, we have 12X - 30X = 216.
Combining like terms, we get -18X = 216.
To isolate X, we can divide both sides of the equation by -18:
X = 216 / -18.
Simplifying the right side of the equation gives us:
X = -12.
So the solution to the equation 1/3 - 5/6 = 1/X is X = -12.
To verify the solution, you can substitute -12 back into the original equation and see if both sides of the equation are equal.