$$ \begin{aligned} \frac{3}{7}(x+3)+5 &= 3x+2&& \text{multiply ALL terms by } \color{blue}{ 7 }. \\[1 em]7 \cdot \frac{3}{7}(x+3)+7\cdot5 &= 7\cdot3x+7\cdot2&& \text{cancel out the denominators} \\[1 em]3x+9+35 &= 21x+14&& \text{simplify left side} \\[1 em]3x+44 &= 21x+14&& \text{move the $ \color{blue}{ 21x } $ to the left side and $ \color{blue}{ 44 }$ to the right} \\[1 em]3x-21x &= 14-44&& \text{simplify left and right hand side} \\[1 em]-18x &= -30&& \text{ divide both sides by $ -18 $ } \\[1 em]x &= \frac{-30}{-18}&& \\[1 em]x &= \frac{5}{3}&& \\[1 em] \end{aligned} $$

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