Solve: \( \frac{2}{7} y+\frac{5}{6}=-\frac{2}{3} y-\frac{5}{6} \)

To solve the equation \( \frac{2}{7} y + \frac{5}{6} = -\frac{2}{3} y - \frac{5}{6} \), we'll start by isolating \( y \). First, let's eliminate the fractions by finding a common denominator for all terms. The least common multiple of 7, 6, and 3 is 42. Multiplying the entire equation by 42 gives: \[ 42 \left(\frac{2}{7} y\right) + 42 \left(\frac{5}{6}\right) = 42 \left(-\frac{2}{3} y\right) - 42 \left(\frac{5}{6}\right) \] This simplifies to: \[ 12y + 35 = -28y - 35 \] Next, let's add \( 28y \) to both sides: \[ 12y + 28y + 35 = -35 \] Combining like terms results in: \[ 40y + 35 = -35 \] Now, we subtract 35 from both sides: \[ 40y = -35 - 35 \] This results in: \[ 40y = -70 \] Now, we divide both sides by 40: \[ y = -\frac{70}{40} \] Simplifying this gives: \[ y = -\frac{7}{4} \] So the solution is: \[ y = -\frac{7}{4} \]