$$\left. \begin{array} { l } { \frac { x + 5 } { 6 } - \frac { x + 1 } { 9 } = \frac { x + 3 } { 4 } } \end{array} \right.$$
$x=-\frac{1}{7}\approx -0.142857143$
$$6\left(x+5\right)-4\left(x+1\right)=9\left(x+3\right)$$
$$6x+30-4\left(x+1\right)=9\left(x+3\right)$$
$$6x+30-4x-4=9\left(x+3\right)$$
$$2x+30-4=9\left(x+3\right)$$
$$2x+26=9\left(x+3\right)$$
$$2x+26=9x+27$$
$$2x+26-9x=27$$
$$-7x+26=27$$
$$-7x=27-26$$
$$-7x=1$$
$$x=\frac{1}{-7}$$
$$x=-\frac{1}{7}$$
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