$$-5 \frac{ 4 }{ 7 } +(- \frac{ 5 }{ 14 } +z)=3 \frac{ 1 }{ 7 }$$
$z = \frac{127}{14} = 9\frac{1}{14} \approx 9.071428571$
$$-2\left(5\times 7+4\right)-5+14z=2\left(3\times 7+1\right)$$
$$-2\left(35+4\right)-5+14z=2\left(3\times 7+1\right)$$
$$-2\times 39-5+14z=2\left(3\times 7+1\right)$$
$$-78-5+14z=2\left(3\times 7+1\right)$$
$$-83+14z=2\left(3\times 7+1\right)$$
$$-83+14z=2\left(21+1\right)$$
$$-83+14z=2\times 22$$
$$-83+14z=44$$
$$14z=44+83$$
$$14z=127$$
$$z=\frac{127}{14}$$
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