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How could we solve $x$, in $|x+1|-|1-x|=2$?

Please suggest a analytical way that I could use in other problems too like this $ |x+1|+|1-x|=2$ and of this genre.

Thank you,

  • 8
    In general, it is best to split problems like this into cases to get rid of the absolute values. Solve the equation first for $x \leq -1$. Then solve it for $-1 \leq x \leq 1$. Finally treat the case $1 \leq x$. This way you find all the possible solutions.2012-01-11
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    Answers to [this question](http://math.stackexchange.com/questions/95465/solving-an-equation-with-absolute-values) mention several methods that can be used for solving such equations.2012-01-11
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    The equation you proposed is a very special case, where the solution can be seen almost immediately from the geometrical meaning. Just notice that the LHS is the difference between the distance of the point $x$ from the point $1$ and the distance of the point $x$ from the point $-1$.2012-01-11
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    You can write the equation $|x+1| - |x-1| = |(x+1)-(x-1)|$.2012-11-14

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