$$34 = \frac{1}{2}(x+6)+3x+2$$

$$ \begin{aligned} 34 &= \frac{1}{2}(x+6)+3x+2&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot34 &= 2 \cdot \frac{1}{2}(x+6)+2(3x+2)&& \text{cancel out the denominators} \\[1 em]68 &= x+6+6x+4&& \text{simplify right side} \\[1 em]68 &= 7x+10&& \text{ swap the left and right side of the equation } \\[1 em]7x+10 &= 68&& \text{ move 10 to the right } \\[1 em]7x &= 68-10&& \\[1 em]7x &= 58&& \text{ divide both sides by $ 7 $ } \\[1 em]x &= \frac{58}{7}&& \\[1 em] \end{aligned} $$

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