Final answer:
The equation -5/6 = 1/2 - 2/3c is solved by finding a common denominator and isolating c. The solution for c is the improper fraction 2, simplified from 2/1.
Step-by-step explanation:
To solve the equation -5/6 = 1/2 - 2/3c for c, we should first aim to combine the fractions on the right side of the equation. This will involve finding a common denominator, which is 6 in this case.
First, we express each fraction with a denominator of 6: 1/2 becomes 3/6 (because 1/2 is equivalent to 3/6) and 2/3c becomes 4/6c (because 2/3 * 2/2 is equivalent to 4/6).
Our equation now looks like: -5/6 = 3/6 - 4/6c. To isolate c, we subtract 3/6 from both sides:
-5/6 - 3/6 = - 4/6c
-8/6 = - 4/6c (Combine like fractions)
Finally, we divide both sides by -4/6 to find c:
c = (-8/6) / (-4/6)
c = 2/1 or simply 2.
The solution for c is 2, expressed as an improper fraction in its simplest form.