$$\frac { 4 x - 1 } { 5 } - \frac { x } { 8 } = 2 \frac { 1 } { 2 }$$
$x=4$
$$8\left(4x-1\right)-5x=20\left(2\times 2+1\right)$$
$$32x-8-5x=20\left(2\times 2+1\right)$$
$$27x-8=20\left(2\times 2+1\right)$$
$$27x-8=20\left(4+1\right)$$
$$27x-8=20\times 5$$
$$27x-8=100$$
$$27x=100+8$$
$$27x=108$$
$$x=\frac{108}{27}$$
$$x=4$$
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