решить неравенство алгебраическим и графическим способами[latex]||x-4|-2| меньше 3[/latex]

[latex]||x-4|-2|<3[/latex] [latex] \left[\begin{array}{ccc} \left \{ {{x-4 \geq 0} \atop {|x-4-2|<3}} \right.\\ \left \{ {{x-4<0} \atop {|-x+4-2|<3}} \right. \end{array}\right[/latex] Решаем отдельно [latex] \left \{ {{x-4 \geq 0} \atop { \left[\begin{array}{ccc} \left \{ {{x-4-2 \geq 0} \atop {x-4-2<3}} \right. \\ \left \{ {{x-4-2<0} \atop {-x+4+2<3}} \right. \end{array}\right}} \right. [/latex] [latex] \left \{ {{x-4-2 \geq 0} \atop {x-4-2<3}} \right. \to \left \{ {{x \geq 6} \atop {x<9}} \right. \to[6;9)[/latex] Вторая система [latex] \left \{ {{x-4-2<0} \atop {-x+4+2<3}} \right. \to \left \{ {{x<6} \atop {x>3}} \right. \to (3;6)[/latex] Теперь  [latex] \left \{ {{x-4<0} \atop { \left[\begin{array}{ccc} \left \{ {{-x+4-2 \geq 0} \atop {-x+4-2<3}} \right. \\ \left \{ {{-x+4-2<0} \atop {x-4+2<3}} \right. \end{array}\right}} \right. [/latex] Решив отдельно, получаем [latex] \left \{ {{-x+4-2 \geq 0} \atop {-x+4-2<3}} \right. \to \left \{ {{x \leq 2} \atop {x>-1}} \right. \to(-1;2][/latex] Второе [latex] \left \{ {{-x+4-2<0} \atop {x-4+2<3}} \right. \to \left \{ {{x>2} \atop {x<5}} \right. \to (-1;5)[/latex] Объеденим и получаем ответ Ответ: [latex](-1;9)[/latex]