$$ \begin{aligned} 2x-\frac{1}{3}+4 &= x+\frac{5}{2}&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6\cdot2x-6\cdot\frac{1}{3}+6\cdot4 &= 6x+6\cdot\frac{5}{2}&& \text{cancel out the denominators} \\[1 em]12x-2+24 &= 6x+15&& \text{simplify left side} \\[1 em]12x+22 &= 6x+15&& \text{move the $ \color{blue}{ 6x } $ to the left side and $ \color{blue}{ 22 }$ to the right} \\[1 em]12x-6x &= 15-22&& \text{simplify left and right hand side} \\[1 em]6x &= -7&& \text{ divide both sides by $ 6 $ } \\[1 em]x &= -\frac{7}{6}&& \\[1 em] \end{aligned} $$

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