Questions: Solve for (y). [ frac32 y-frac78=-frac73 ]

Solution Steps

To solve for \( y \) in the given equation, we need to isolate \( y \). First, we will move the constant term \(-\frac{7}{8}\) to the other side of the equation by adding \(\frac{7}{8}\) to both sides. Then, we will multiply both sides by the reciprocal of \(\frac{3}{2}\) to solve for \( y \).

We start with the equation: \[ \frac{3}{2} y - \frac{7}{8} = -\frac{7}{3} \] To isolate \( y \), we add \( \frac{7}{8} \) to both sides: \[ \frac{3}{2} y = -\frac{7}{3} + \frac{7}{8} \]

Next, we need to combine the fractions on the right side. The common denominator for \( 3 \) and \( 8 \) is \( 24 \): \[ -\frac{7}{3} = -\frac{56}{24}, \quad \frac{7}{8} = \frac{21}{24} \] Thus, we have: \[ \frac{3}{2} y = -\frac{56}{24} + \frac{21}{24} = -\frac{35}{24} \]

Now, we multiply both sides by the reciprocal of \( \frac{3}{2} \), which is \( \frac{2}{3} \): \[ y = -\frac{35}{24} \cdot \frac{2}{3} = -\frac{70}{72} = -\frac{35}{36} \]

Final Answer