$$ \begin{aligned} \frac{1}{2} &= 3x+4&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot\frac{1}{2} &= 2\cdot3x+2\cdot4&& \text{cancel out the denominators} \\[1 em]1 &= 6x+8&& \text{ swap the left and right side of the equation } \\[1 em]6x+8 &= 1&& \text{ move 8 to the right } \\[1 em]6x &= 1-8&& \\[1 em]6x &= -7&& \text{ divide both sides by $ 6 $ } \\[1 em]x &= -\frac{7}{6}&& \\[1 em] \end{aligned} $$

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