e. \( \frac{5}{10} x+9=\frac{4}{3}-\left(x-\frac{7}{3}\right) \)

To solve the equation \( \frac{5}{10} x + 9 = \frac{4}{3} - \left( x - \frac{7}{3} \right) \), we can start by simplifying the equation. Firstly, note that \( \frac{5}{10} \) simplifies to \( \frac{1}{2} \), so rewrite the equation as \( \frac{1}{2} x + 9 = \frac{4}{3} - (x - \frac{7}{3}) \). Next, distribute the negative sign on the right side of the equation: \[ \frac{1}{2} x + 9 = \frac{4}{3} - x + \frac{7}{3} \] \[ \frac{1}{2} x + 9 = \frac{11}{3} - x \] Now, move all terms involving \( x \) to one side and constants to the other side: \[ \frac{1}{2} x + x = \frac{11}{3} - 9 \] \[ \frac{3}{2} x = \frac{11}{3} - \frac{27}{3} \] \[ \frac{3}{2} x = \frac{-16}{3} \] To isolate \( x \), multiply both sides by the reciprocal of \( \frac{3}{2} \), which is \( \frac{2}{3} \): \[ x = \frac{-16}{3} \times \frac{2}{3} = \frac{-32}{9} \] So the solution is \( x = \frac{-32}{9} \).