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Solve for x: 3x+2/7 + 4(x+1)/5 =2/3(2x+1).

$\frac{3 x + 2}{7} + \frac{4 (x + 1)}{5} = \frac{2}{3} (2 x + 1) \Rightarrow \frac{5 (3 x + 2) + 7 (4 x + 4)}{7 \times 5} = \frac{4 x + 2}{3} \Rightarrow \frac{15 x + 10 + 28 x + 28}{35} = \frac{4 x + 2}{3} \Rightarrow 3 (43 x + 38) = 35 (4 x + 2) \Rightarrow 129 x + 114 = 140 x + 70 \Rightarrow 140 x - 129 x = 114 - 70 \Rightarrow 11 x = 44 \Rightarrow x = \frac{44}{11} = 4$

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