\(\dfrac{x-1}{5}+\dfrac{x-2}{6}+\dfrac{x-3}{7}=-3\\ \left(\dfrac{x-1}{5}+1\right)+\left(\dfrac{x-2}{6}+1\right)+\left(\dfrac{x-3}{7}+1\right)=-3+3\\ \dfrac{x+4}{5}+\dfrac{x+4}{6}+\dfrac{x+4}{7}=0\\ \left(x+4\right)\left(\dfrac{1}{5}+\dfrac{1}{6}+\dfrac{1}{7}\right)=0\\ x+4=0\\ x=-4\)
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