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Hello people I've got some problems to solve this equation

$$ |f(x)| - |g(x)| + |h(x)| = \begin{cases} -1 &\text{if } x < -1 \\ 3x + 2 &\text{if } -1 < x <0 \\ -2x + 2 &\text{if } x > 0 \end{cases} $$

I tried to solve the system but I'm stuck, so I'm counting on you for help me thanks.

PS: I'm looking for web ressources in order to improve myself in math if you have an idea do not heasitate.

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    $\begingroup$ I'm not sure what solution means for your Question. It doesn't seem to mean "solve a system of equations" for $x$ as an unknown. $\endgroup$ – hardmath Jan 16 '18 at 21:35
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Let   $ \displaystyle\, k(x) = \begin{cases} -1 &\text{if } x < -1 \\ 3x + 2 &\text{if } -1 < x <0 \\ -2x + 2 &\text{if } x > 0 \end{cases} \,$   and define  $\,\begin{cases}f(x)=\frac{1}{2}\big(k(x) + |k(x)|\big) \\ g(x)=\frac{1}{2}\big(k(x) - |k(x)|\big) \\ h(x)=0 \end{cases}\,$
then show that:

  • $f(x) \ge 0$

  • $g(x) \le 0$

  • $|f(x)| - |g(x)| + |h(x)| = f(x) + g(x) = k(x)$

P.S. To the OP, if this is not the kind of answer you were looking for, please clarify the question.

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