[tex]\dfrac{2}{3}\cdot x +\dfrac{1}{2} = \dfrac{3}{4}\Big|\cdot 3\cdot 2\cdot 4\\ \\ \Rightarrow (3\cdot 2\cdot 4)\cdot \dfrac{2}{3}\cdot x+(3\cdot 2\cdot 4)\cdot \dfrac{1}{2} = (3\cdot 2\cdot 4)\cdot \dfrac{3}{4}\\ \\ \Rightarrow (2\cdot 4)\cdot 2\cdot x + (3\cdot 4)\cdot 1 = (3\cdot 2)\cdot 3\\ \\ \Rightarrow 16x+12 = 18\\ \\ \Rightarrow 16x = 18-12\\ \\ \Rightarrow 16x = 6\\ \\ \Rightarrow x = \dfrac{6}{16}\\ \\ \Rightarrow \boxed{x = \dfrac{3}{8}}[/tex]
