$$ \begin{aligned} 6 \cdot \frac{x+1}{4} &= 3x-1&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4\cdot6 \cdot \frac{x+1}{4} &= 4\cdot3x-4\cdot1&& \text{cancel out the denominators} \\[1 em]6x+6 &= 12x-4&& \text{move the $ \color{blue}{ 12x } $ to the left side and $ \color{blue}{ 6 }$ to the right} \\[1 em]6x-12x &= -4-6&& \text{simplify left and right hand side} \\[1 em]-6x &= -10&& \text{ divide both sides by $ -6 $ } \\[1 em]x &= \frac{-10}{-6}&& \\[1 em]x &= \frac{5}{3}&& \\[1 em] \end{aligned} $$

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