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Prove It You might have to use the triangle inequality here...
$\displaystyle \displaystyle x \leq |x - 1| + |x - 2| - |x + 3|$
$\displaystyle \displaystyle x \leq |x| + |-1| + |x| + |-2| - (|x| + |3|)$, since $\displaystyle \displaystyle |a + b| \leq |a| + |b|$ by the Triangle Inequality
$\displaystyle \displaystyle x \leq |x| + 1 + |x| + 2 - |x| - 3$
$\displaystyle \displaystyle x \leq |x|$.
A number is only ever less than its absolute value if it's negative, so
$\displaystyle \displaystyle x \leq 0$.