$$\frac { 7 x - 10 } { x - 2 } = 7 \frac { 1 } { 2 }$$
$x=10$
$$2\left(7x-10\right)=\left(x-2\right)\left(7\times 2+1\right)$$
$$14x-20=\left(x-2\right)\left(7\times 2+1\right)$$
$$14x-20=\left(x-2\right)\left(14+1\right)$$
$$14x-20=\left(x-2\right)\times 15$$
$$14x-20=15x-30$$
$$14x-20-15x=-30$$
$$-x-20=-30$$
$$-x=-30+20$$
$$-x=-10$$
$$x=10$$
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