$$ \begin{aligned} \frac{3}{7}(x+3)+5 &= 3\cdot2&& \text{multiply ALL terms by } \color{blue}{ 7 }. \\[1 em]7 \cdot \frac{3}{7}(x+3)+7\cdot5 &= 7\cdot3\cdot2&& \text{cancel out the denominators} \\[1 em]3x+9+35 &= 42&& \text{simplify left side} \\[1 em]3x+44 &= 42&& \text{ move 44 to the right } \\[1 em]3x &= 42-44&& \\[1 em]3x &= -2&& \text{ divide both sides by $ 3 $ } \\[1 em]x &= -\frac{2}{3}&& \\[1 em] \end{aligned} $$

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