Question: Solve for y. \frac{1}{3}y - 4 = -\frac{3}{5}y - \frac{7}{5} Simplify your answer as much as…

Solve for y. \frac{1}{3}y - 4 = -\frac{3}{5}y - \frac{7}{5} Simplify your answer as much as possible. y = \boxed{\quad}

Solution

To solve for \( y \) in the equation \[ \frac{1}{3}y - 4 = \frac{3}{5}y - \frac{7}{5} \] First, eliminate the fractions by finding the least common multiple (LCM) of the denominators, which is 15. Multiply every term by 15: \[ 15 \left(\frac{1}{3}y\right) - 15 \times 4 = 15 \left(\frac{3}{5}y\right) - 15 \left(\frac{7}{5}\right) \] This simplifies to: \[ 5y - 60 = 9y - 21 \] Next, move all terms involving \( y \) to one side of the equation and constant terms to the other side: \[ 5y - 9y = -21 + 60 \] Simplify both sides: \[ -4y = 39 \] Divide both sides by -4 to solve for \( y \): \[ y = -\frac{39}{4} \] Thus, the solution is \( y = -\frac{39}{4} \).