$$ \begin{aligned} 7x+\frac{6}{2} &= 3x+2&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot7x+2\cdot\frac{6}{2} &= 2\cdot3x+2\cdot2&& \text{cancel out the denominators} \\[1 em]14x+6 &= 6x+4&& \text{move the $ \color{blue}{ 6x } $ to the left side and $ \color{blue}{ 6 }$ to the right} \\[1 em]14x-6x &= 4-6&& \text{simplify left and right hand side} \\[1 em]8x &= -2&& \text{ divide both sides by $ 8 $ } \\[1 em]x &= -\frac{2}{8}&& \\[1 em]x &= -\frac{1}{4}&& \\[1 em] \end{aligned} $$

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