The given equation is: $$|x - |4-x|| -2x = 4.$$ (Here $|x|$ means the absolute value of $x [\text{abs}(x)])$ Please help me to solve the equation for $x$.
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Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. Also, see this MathJax Tutorial to learn how to write equations here in a more readable way. – mzp Apr 28 '18 at 18:52
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Thanks. I will see to them in my next questions. – tomriddle99 Apr 28 '18 at 19:22
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$|4-x|$ is either $4-x$ or $x-4$. In the first case, we want to solve $|x-(4-x)|-2x=4$, in the other $|x-(x-4)|-2x=4$. In the latter case, $|x-(x-4)|$ is simply $4$, and $4-2x=4$ has the only solution $x=0$. In the first case again, $|x-(4-x)|$ is either $2x-4$ or $4-2x$, so we want to solve $-4=4$ (nope) or $4-4x=4$ (leads to $x=0$). So we only find $x=0$ as candidate solution and readily verify that it actually solves the original equation.
Hagen von Eitzen
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