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QUESTION

Determine the values of $x$ satisfying $x-2<1-x<2x$.

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ANSWER

$\ds -2+x<1-x<2x\\ -2+x<1-x\Rightarrow2x<3,\ x<\frac{3}{2}\\
1-x<2x\Rightarrow3x>1,\ x>\frac{1}{3}$\\so the solution is
$\ds\frac{1}{3}<x<\frac{3}{2}$.




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