[tex]\displaystyle\bf\\\frac{x+3}{6} +\frac{6-x}{21} =\frac{x+7}{14} \\\\\\\frac{x+3}{6} +\frac{6-x}{21} -\frac{x+7}{14} =0\\\\\\\frac{x+3}{6} \cdot 42+\frac{6-x}{21}\cdot 42 -\frac{x+7}{14}\cdot 42=0\\\\\\7\cdot(x+3)+2\cdot(6-x)-3\cdot(x+7)=0\\\\7x+21+12-2x-3x-21=0\\\\7x-2x-3x=-21-12+21\\\\2x=-12\\\\x=-12:2\\\\\boxed{x=-6}[/tex]