$$\frac{2x+2}{5}=\frac{4x-7}{6}$$
$x = \frac{47}{8} = 5\frac{7}{8} = 5.875$
$$6\left(2x+2\right)=5\left(4x-7\right)$$
$$12x+12=5\left(4x-7\right)$$
$$12x+12=20x-35$$
$$12x+12-20x=-35$$
$$-8x+12=-35$$
$$-8x=-35-12$$
$$-8x=-47$$
$$x=\frac{-47}{-8}$$
$$x=\frac{47}{8}$$
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