$$ \begin{aligned} 4x+\frac{1}{3}-2x+\frac{1}{2} &= 6&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6\cdot4x+6\cdot\frac{1}{3}-6\cdot2x+6\cdot\frac{1}{2} &= 6\cdot6&& \text{cancel out the denominators} \\[1 em]24x+2-12x+3 &= 36&& \text{simplify left side} \\[1 em]12x+5 &= 36&& \text{ move 5 to the right } \\[1 em]12x &= 36-5&& \\[1 em]12x &= 31&& \text{ divide both sides by $ 12 $ } \\[1 em]x &= \frac{31}{12}&& \\[1 em] \end{aligned} $$

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