5/12(c-3)-1/6(2c-7)=2

To solve the equation \(\frac{5}{12}(c - 3) - \frac{1}{6}(2c - 7) = 2\), we will start by eliminating the fractions to make the equation easier to work with. First, let's find a common denominator for the fractions. The least common multiple of 12 and 6 is 12. We can multiply the entire equation by 12 to eliminate the denominators: \[ 12 \left( \frac{5}{12}(c - 3) \right) - 12 \left( \frac{1}{6}(2c - 7) \right) = 12 \cdot 2 \] This simplifies to: \[ 5(c - 3) - 2(2c - 7) = 24 \] Now, distribute on the left side: \[ 5c - 15 - 4c + 14 = 24 \] Combine like terms: \[ (5c - 4c) + (-15 + 14) = 24 \] This simplifies to: \[ c - 1 = 24 \] Now, add 1 to both sides to solve for \(c\): \[ c = 25 \] Thus, the solution to the equation is: \[ \boxed{25} \]