Questions: Solve the following equation. Express your answer as an integer, simplified fraction, or decimal rounded to two decimal places. 5/12 y - 7/6 y + 4/5 = 1/4

Solution Steps

We start with the equation: \[ \frac{5}{12} y - \frac{7}{6} y + \frac{4}{5} = \frac{1}{4} \] First, we combine the terms involving \( y \). The coefficients of \( y \) can be expressed with a common denominator: \[ \frac{5}{12} y - \frac{14}{12} y = -\frac{9}{12} y = -\frac{3}{4} y \] Thus, the equation simplifies to: \[ -\frac{3}{4} y + \frac{4}{5} = \frac{1}{4} \]

Next, we isolate \( y \) by moving the constant term to the right side: \[ -\frac{3}{4} y = \frac{1}{4} - \frac{4}{5} \] To perform the subtraction, we find a common denominator (20): \[ \frac{1}{4} = \frac{5}{20}, \quad \frac{4}{5} = \frac{16}{20} \] Thus, we have: \[ -\frac{3}{4} y = \frac{5}{20} - \frac{16}{20} = -\frac{11}{20} \]

Now, we solve for \( y \) by multiplying both sides by \(-\frac{4}{3}\): \[ y = -\frac{11}{20} \cdot -\frac{4}{3} = \frac{44}{60} = \frac{11}{15} \]

Final Answer