Solve the equation. \( \frac{5}{6} x-2 x+\frac{8}{3}=\frac{5}{3} \)

To solve the equation \( \frac{5}{6} x - 2x + \frac{8}{3} = \frac{5}{3} \), we start by combining like terms. First, we'll express \( 2x \) as \( \frac{12}{6} x \) to have a common denominator: \[ \frac{5}{6} x - \frac{12}{6} x + \frac{8}{3} = \frac{5}{3} \] Combine the \( x \) terms: \[ \left(\frac{5}{6} - \frac{12}{6}\right) x + \frac{8}{3} = \frac{5}{3} \] This simplifies to: \[ -\frac{7}{6} x + \frac{8}{3} = \frac{5}{3} \] Next, subtract \( \frac{8}{3} \) from both sides: \[ -\frac{7}{6} x = \frac{5}{3} - \frac{8}{3} \] Combining the fractions on the right side gives: \[ -\frac{7}{6} x = -\frac{3}{3} = -1 \] Now, multiply both sides by -1: \[ \frac{7}{6} x = 1 \] To solve for \( x \), multiply both sides by the reciprocal of \( \frac{7}{6} \), which is \( \frac{6}{7} \): \[ x = 1 \times \frac{6}{7} = \frac{6}{7} \] Thus, the solution to the equation is: \[ \boxed{\frac{6}{7}} \]