Question

|х+5| больше или равно 6х

Answer 1

По определению абсолютной величины:

$\displaystyle \left[\displaystyle\begin{array}{ccc}\left \{ {{x+5\geq 0} \atop {x+5\geq 6x}} \right.\\ \\ \left \{ {{x+5<0} \atop {-(x+5)\geq 6x}} \right.\end{array}\right~~~\Rightarrow~~~\left[\begin{array}{ccc}\left \{ {{x\geq -5} \atop {-5x\geq -5}} \right.\\ \\ \left \{ {{x<-5} \atop {-7x\geq 5}} \right.\end{array}\right~~~\Rightarrow~~~\left[\begin{array}{ccc}\left \{ {{x\geq -5} \atop {x\leq 1}} \right.\\ \\ \left \{ {{x<-5} \atop {x\leq -\frac{5}{7}}} \right.\end{array}\right$

$\Rightarrow~~\left[\begin{array}{ccc}-5\leq x\leq 1\\ \\ x< -5\end{array}\right~~~\Rightarrow~~~ x\leq 1$

Ответ: x ∈ (-∞; 1]