$$6x-\frac{2}{9}+3x+\frac{5}{18} = \frac{1}{3}$$

$$ \begin{aligned} 6x-\frac{2}{9}+3x+\frac{5}{18} &= \frac{1}{3}&& \text{multiply ALL terms by } \color{blue}{ 18 }. \\[1 em]18\cdot6x-18\cdot\frac{2}{9}+18\cdot3x+18\cdot\frac{5}{18} &= 18\cdot\frac{1}{3}&& \text{cancel out the denominators} \\[1 em]108x-4+54x+5 &= 6&& \text{simplify left side} \\[1 em]162x+1 &= 6&& \text{ move 1 to the right } \\[1 em]162x &= 6-1&& \\[1 em]162x &= 5&& \text{ divide both sides by $ 162 $ } \\[1 em]x &= \frac{5}{162}&& \\[1 em] \end{aligned} $$

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