Question

Решите уравнение
|x-3| - |2x-4| = -5

Answer 1

|x-3| - |2x-4| = -5
х-3=0         2х-4=0
х=3            2х=4
                  х=2
___________________2_____________3____________

1) x<2             -(x-3)+(2x-4)=-5
                       -x+3+2x-4=-5
                       x-1=-5
                       x=-5+1
                       x=-4 <2
                       x=-4 -корень уравнения
2) 2<x<3         -(x-3)-(2x-4)=-5
                       -x+3-2x+4=-5
                       -3x+7=-5
                       -3x=-5-7
                       -3x=-12 |:(-3)
                        x=4 ∈ (2;3)
                        x=4 - не является корнем уравнения
3) x>3             +(x+3)-(2x-4)=-5
                        x+3-2x+4=-5
                       -x+7=-5
                       -x=-5-7
                       -x=-12 |:(-1)
                        x=12 ∈ (3;+∞)
                        x=12 -корень уравнения
Ответ: -4 и 12