12. Solve the equation. (5)/(6)x-3x+(4)/(3)=(5)/(3) The solution set is square (Simplify your answer.)

To solve the equation, we first combine like terms on the left side of the equation:<br /><br />$\frac{5}{6}x - 3x + \frac{4}{3} = \frac{5}{3}$<br /><br />Combine the x terms:<br /><br />$\frac{5}{6}x - 3x = \frac{5}{3} - \frac{4}{3}$<br /><br />Simplify the right side:<br /><br />$\frac{5}{6}x - 3x = \frac{1}{3}$<br /><br />Combine the x terms on the left side:<br /><br />$\frac{5}{6}x - \frac{18}{6}x = \frac{1}{3}$<br /><br />Simplify the left side:<br /><br />$-\frac{13}{6}x = \frac{1}{3}$<br /><br />Divide both sides by $-\frac{13}{6}$:<br /><br />$x = \frac{1}{3} \div -\frac{13}{6}$<br /><br />Simplify the right side:<br /><br />$x = -\frac{2}{13}$<br /><br />Therefore, the solution set is $\boxed{-\frac{2}{13}}$.