1. (16 points) Solve the equation $x-5=\frac{3 \cdot|x-2|}{x-2}$. If the equation has multiple roots, write their sum in the answer.

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# Answer: 8.

Solution. The equation has a restriction on the variable $x \neq 2$. We open the modulus: for $x>2, x-5=3, x=8$. For $x<2, \quad x-5=-3, x=2$ - an extraneous root.