$$m-\frac{M-1}{2}=1-\frac{x-2}{3}$$
$M=\frac{2x}{3}+2m-\frac{7}{3}$
$$6m-3\left(M-1\right)=6-2\left(x-2\right)$$
$$6m-3M+3=6-2\left(x-2\right)$$
$$6m-3M+3=6-2x+4$$
$$6m-3M+3=10-2x$$
$$-3M+3=10-2x-6m$$
$$-3M=10-2x-6m-3$$
$$-3M=7-2x-6m$$
$$-3M=7-6m-2x$$
$$\frac{-3M}{-3}=\frac{7-6m-2x}{-3}$$
$$M=\frac{7-6m-2x}{-3}$$
$$M=\frac{2x}{3}+2m-\frac{7}{3}$$
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$m=\frac{M}{2}-\frac{x}{3}+\frac{7}{6}$
$$6m+3=10-2x+3M$$
$$6m=10-2x+3M-3$$
$$6m=7-2x+3M$$
$$6m=7+3M-2x$$
$$\frac{6m}{6}=\frac{7+3M-2x}{6}$$
$$m=\frac{7+3M-2x}{6}$$
$$m=\frac{M}{2}-\frac{x}{3}+\frac{7}{6}$$
