$$\left. \begin{array} { l } { \frac { 4 x + 1 } { 3 } + \frac { 2 x + 1 } { 2 } = \frac { 3 x - 7 } { 5 } + 6 } \end{array} \right.$$
$x = \frac{113}{52} = 2\frac{9}{52} \approx 2.173076923$
$$10\left(4x+1\right)+15\left(2x+1\right)=6\left(3x-7\right)+180$$
$$40x+10+15\left(2x+1\right)=6\left(3x-7\right)+180$$
$$40x+10+30x+15=6\left(3x-7\right)+180$$
$$70x+10+15=6\left(3x-7\right)+180$$
$$70x+25=6\left(3x-7\right)+180$$
$$70x+25=18x-42+180$$
$$70x+25=18x+138$$
$$70x+25-18x=138$$
$$52x+25=138$$
$$52x=138-25$$
$$52x=113$$
$$x=\frac{113}{52}$$
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