Answer: The required solution for x is \(-\dfrac{11}{6}.\)
Step-by-step explanation: We are given to solve the following equation for x :
\(-\dfrac{2}{3}(3x-4)+3x=\dfrac{5}{6}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)
To solve the given equation for x,
we must take all the terms involving x on the left-hand side and the other constant terms on the right-hand side of the equation.
The solution of equation (i) is as follows :
\(-\dfrac{2}{3}(3x-4)+3x=\dfrac{5}{6}\\\\\\\Rightarrow -2x+\dfrac{8}{3}+3x=\dfrac{5}{6}\\\\\\\Rightarrow x=\dfrac{5}{6}-\dfrac{8}{3}\\\\\\\Rightarrow x=\dfrac{5-16}{6}\\\\\\\Rightarrow x=-\dfrac{11}{6}.\)
Thus, the required solution for x is \(-\dfrac{11}{6}.\)
