Hello,

I have read the sticky thread about solving inequalities, but still I cannot solve this one:

$\displaystyle |x-1|+|x-2|-|x+3|>=x$

Thanks in advance!

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- Feb 25th 2011, 10:00 PMmsokol89Solving inequation with 3 absolute values
Hello,

I have read the sticky thread about solving inequalities, but still I cannot solve this one:

$\displaystyle |x-1|+|x-2|-|x+3|>=x$

Thanks in advance! - Feb 25th 2011, 10:04 PMProve 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

$\displaystyle \displaystyle x \leq 0$. - Feb 25th 2011, 11:25 PMmsokol89