$$\frac{2}{3}x+3=x+2$$
$x=3$
$$\frac{2}{3}x+3-x=2$$
$$-\frac{1}{3}x+3=2$$
$$-\frac{1}{3}x=2-3$$
$$-\frac{1}{3}x=-1$$
$$x=-\left(-3\right)$$
$$x=3$$
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