(c) \( \frac{y-2}{2}-\frac{y+1}{3}=\frac{1}{4} \)

To solve the equation \( \frac{y-2}{2}-\frac{y+1}{3}=\frac{1}{4} \), first find a common denominator for the fractions, which is 12. Rewrite each term: \[ \frac{6(y-2)}{12} - \frac{4(y+1)}{12} = \frac{3}{12} \] Now combine the fractions: \[ \frac{6(y-2) - 4(y+1)}{12} = \frac{3}{12} \] Multiply both sides by 12 to eliminate the denominator: \[ 6(y-2) - 4(y+1) = 3 \] Distribute: \[ 6y - 12 - 4y - 4 = 3 \] Combine like terms: \[ 2y - 16 = 3 \] Add 16 to both sides: \[ 2y = 19 \] Finally, divide by 2: \[ y = \frac{19}{2} \] So, the solution is \( y = 9.5 \). Did you know that fractional equations like this can often feel daunting, but breaking them down into smaller parts can make them much easier to manage? It's like piecing together a puzzle—each step brings you closer to the finished picture! In everyday life, you might encounter similar equations when dealing with finances, like calculating shared expenses or splitting bills. Understanding how to manipulate these fractions can really come in handy during meal outings or trips!