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Please, can someone help me to solve this:
|x - 2| = 1/e
I really don't know the way in which I could solve an absolute value.

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    For the intuition, it is useful to know that $|x-2|$ is the **distance** between $x$ and $2$. This distance is $1/e$ precisely when $x=2+1/e$ and when $x=2-1/e$, that is, $1/e$ to the right and $1/e$ to the left of $2$. (I am assuming that by $e$ you mean the base for the natural logarithms.)2011-12-14

1 Answers 1

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From the definition of absolute value, $x$ is a solution of $\tag{1}|x-2|={1\over e}$ if and only if $\tag{2}x-2={1\over e}$ or $\tag{3}-(x-2)={1\over e}.$ (Since $|x-2|$ is either $x-2$ or $-(x-2)\,$.)

For emphasis: if $a$ is a solution of either equation (2) or equation (3), it must be a solution of equation (1). On the other hand, if $a$ is a solution of equation (1), it must be a solution of one of equations (2) or (3).

So, the solution set of equation (1) is precisely the union of the solution sets to equations (1) and (2).

You need to solve both of equations (1) and (2) (which I leave to you). Then you can state that the solutions to equation (1) are all the solutions found in the previous sentence.