Question

Решить уравнение |х-2| - 3|3-х| +х =0

Answer 1

Определим знаки подмодульных выражений

x - 2 = 0; x = 2

3 - x = 0; x = 3

____- +_____(2)____+ +____(3)____+ -_____

$\displaystyle \left[\begin{array}{ccc}\displaystyle \left \{ {{x\leq 2} \atop {-(x-2)-3(3-x)+x=0}} \right.\\ \displaystyle \left \{ {{2<x\leq 3} \atop {x-2-3(3-x)+x=0}} \right.\\ \displaystyle \left \{ {{x>3} \atop {x-2+3(3-x)+x=0}} \right.\end{array}\right~~\Rightarrow~\left[\begin{array}{ccc}\displaystyle \left \{ {{x\leq2} \atop {x=\frac{7}{3}}} \right.\\ \displaystyle \left \{ {{2<x\leq3} \atop {x=2{,}2}} \right.\\ \displaystyle \left \{ {{x>3} \atop {x=7}} \right.\end{array}\right$

$\Rightarrow~~\left[\begin{array}{ccc}\varnothing\\ x=2{,}2\\ x=7\end{array}\right$

Ответ: 2,2; 7.