Final answer:
To solve the given equation (1/4c + 5/3c - 4 = 2 - 1/12) for c, first combine like terms by finding a common denominator and simplify. Move all terms with c to one side and constants to the other to isolate c. Solve for c by multiplying by the reciprocal of the coefficient of c, resulting in c = 71/69.
Step-by-step explanation:
To find the value of c in the equation 1/4c + 5/3c - 4 = 2 - 1/12, we first need to combine like terms and solve for c. Let's break it down step by step:
- Combine like terms by finding a common denominator for the fractions that have c as a variable. In this case, the common denominator for 1/4 and 5/3 is 12. So we rewrite the equation as (3/12)c + (20/12)c - 4 = 2 - 1/12.
- Combine the fractions with c to get (23/12)c - 4 = 2 - 1/12.
- Now, move all terms with c to one side and the constants to the other side. Add 4 to both sides: (23/12)c = 2 - 1/12 + 4.
- Combining the constant terms: 2 + 4 = 6 and - 1/12 is the same as -6/72.
- Adding 6 and -6/72 gives us 6 - 6/72 or (432/72) - (6/72) which simplifies to (426/72), which is (213/36) after further simplification.
- Now we have (23/12)c = (213/36).
- Finally, solve for c by multiplying both sides by the reciprocal of (23/12), which is (12/23): c = (213/36) * (12/23).
- When we multiply these two fractions, we get an answer for c. (213 * 12) / (36 * 23) simplifies to (213/3) / (3 * 23), which further simplifies to 71/69.
- So the solution is c = 71/69.
Note that the correct use of arithmetic and algebra is essential in solving for c in this equation. This process is an example of solving linear equations with fractions.