$$\frac{ 5x-4 }{ 8 } - \frac{ x-3 }{ 5 } = \frac{ x+6 }{ 4 }$$
$x=8$
$$5\left(5x-4\right)-8\left(x-3\right)=10\left(x+6\right)$$
$$25x-20-8\left(x-3\right)=10\left(x+6\right)$$
$$25x-20-8x+24=10\left(x+6\right)$$
$$17x-20+24=10\left(x+6\right)$$
$$17x+4=10\left(x+6\right)$$
$$17x+4=10x+60$$
$$17x+4-10x=60$$
$$7x+4=60$$
$$7x=60-4$$
$$7x=56$$
$$x=\frac{56}{7}$$
$$x=8$$
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