modulus inequality

\hspace{-16}\bf{\mathbb{S}}$olve the inequality\\\\ $\bf{\mid x-1 \mid+3\mid x-3 \mid+5\mid x-5 \mid+.......+2009\mid x-2009\mid}$\\\\\\ $\bf{\geq 2 \mid x-2 \mid+4\mid x-4 \mid+6\mid x-6 \mid+.......+2008\mid x-2008\mid}$

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