$$\frac { 4 x - 3 } { 9 } - \frac { x } { 3 } = \frac { 5 ( x - 1 ) } { 6 }$$
$x=\frac{9}{13}\approx 0.692307692$
$$2\left(4x-3\right)-6x=3\times 5\left(x-1\right)$$
$$8x-6-6x=3\times 5\left(x-1\right)$$
$$2x-6=3\times 5\left(x-1\right)$$
$$2x-6=15\left(x-1\right)$$
$$2x-6=15x-15$$
$$2x-6-15x=-15$$
$$-13x-6=-15$$
$$-13x=-15+6$$
$$-13x=-9$$
$$x=\frac{-9}{-13}$$
$$x=\frac{9}{13}$$
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