[ [ equations with absolute values ]

Solve the equation: $|x-2005|+|2005-x|=2006$.

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The first method. Using the equality of the moduli of opposite numbers, we get that $|\mathrm{x}-2005|=1003$. From this, $\mathrm{x}$ $-2005=±1003$, that is, $x=1002$ or $x=3008$.

The second method. If $x>=2005$, then $2(x-2005)=2006$, from which $x=3008$. If $x<2005$, then $2(2005-x)=2006$, from which $x=1002$.

## Answer

$1002 ; 3008$.