solve for c express your answer as a proper or improper fraction in simplest terms.
-1/2 = 2/11c - 3/4
To solve for c, we need to isolate it on one side of the equation.
Starting with the equation: -1/2 = 2/11c - 3/4
First, let's get rid of the fraction on the right side by finding a common denominator for 2/11c and 3/4. The least common multiple (LCM) of 11 and 4 is 44.
Multiplying the numerator and denominator of 2/11c by 4 gives us 8/44c. Multiplying the numerator and denominator of 3/4 by 11 gives us 33/44.
The equation becomes: -1/2 = 8/44c - 33/44
Now, let's combine the fractions on the right side of the equation by subtracting 33/44 from 8/44c.
-1/2 = (8/44c - 33/44)
To subtract the fractions, we need to have a common denominator of 44c.
-1/2 = (8 - 33c)/(44c)
Next, let's eliminate the denominator by multiplying both sides of the equation by 44c.
(44c) * (-1/2) = (44c) * (8 - 33c)/(44c)
-22c = 8 - 33c
To solve for c, we will move all the terms containing c to one side of the equation and all the constant terms to the other side.
-22c + 33c = 8
11c = 8
Now, divide both sides of the equation by 11 to solve for c.
c = 8/11
Therefore, the solution for c is 8/11.