$$34 = 3x+\frac{x}{3}$$

$$ \begin{aligned} 34 &= 3x+\frac{x}{3}&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3\cdot34 &= 3\cdot3x+3 \cdot \frac{x}{3}&& \text{cancel out the denominators} \\[1 em]102 &= 9x+x&& \text{simplify right side} \\[1 em]102 &= 10x&& \text{ swap the left and right side of the equation } \\[1 em]10x &= 102&& \text{ divide both sides by $ 10 $ } \\[1 em]x &= \frac{102}{10}&& \\[1 em]x &= \frac{51}{5}&& \\[1 em] \end{aligned} $$

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