Question

 решить неравенство алгебраическим и графическим способами
$||x-4|-2|<3$

Answer 1

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

Ответ: $(-1;9)$