Найдите длину промежутка

[latex]|x^2-2x| \leq x+4\\\\\star \; \; \; |x|\ \textless \ a\; \; \Rightarrow \; \; \; -a\ \textless \ x\ \textless \ a\; \; \star \\\\-(x+4) \leq x^2-2x \leq x+4\; \; \Rightarrow \; \; \; \left \{ {{x^2-2x \leq x+4} \atop {x^2-2x \geq -x-4}} \right. \\\\ \left \{ {{x^2-3x-4 \leq 0} \atop {x^2-x+4 \geq 0}} \right. \\\\a)\; \; x^2-3x-4 \leq 0\; ,\; \; \; x_1=-1\; ,\; \; x_2=4\\\\(x+1)(x-4) \leq 0\; \; \; \; +++[-1\, ]---[\, 4\, ]+++\\\\x\in [-1;4\, ]\\\\b)\; \; x^2-x+4 \geq 0[/latex] [latex]D=1-16=-15\ \textless \ 0\; \; \Rightarrow \; \; \; x^2-x+4\ \textgreater \ 0\; pri\; x\in (-\infty ,+\infty )[/latex] [latex]c)\; \; \left \{ {{x\in [-1;4\, ]} \atop {x\in (-\infty ,+\infty )}} \right. \; \; \Rightarrow \; \; \; x\in [-1;4\, ]\\\\d)\; \; dlina\; intervala\; =4-(-1)=5[/latex]