Question

х - 4 = модуль х-2 дробь х -2 Решите уравнение

Answer 1

x-4=Ix-2I/(x-2)

Первый случай:

x-4=(x-2)/(x-2)

x-4=1

x=5

Второй случай:

x-4=-(x-2)/(x-2)

x-4=-1

x=3

Ответ: x=3; x=5

Answer 2

$x-4=\frac {|x-2|}{x-2};$

если х-2>0 т.е. x>2, то |x-2|=x-2 и уравнение принимает вид

x-4=1

x=4+1

x=5 - удовлетворяет

 

если х-2<0 т.е. x<2, то |x-2|=-(x-2) и уравнение принимает вид

x-4=-1

x=4-1

x=3 - не удовлетворяет

 

ответ: 5

Answer 3

Problem Analysis

We are given the equation x - 4 = |x - 2| + (x - 2) and we need to solve for x.

Solution

To solve the equation, we can consider two cases: when x - 2 is positive and when it is negative.

Case 1: x - 2 > 0 In this case, the equation becomes x - 4 = x - 2 + (x - 2). Simplifying the equation, we get: x - 4 = x - 2 + x - 2 x - 4 = 3x - 6 2x = 2 x = 1

Case 2: x - 2 < 0 In this case, the equation becomes x - 4 = -(x - 2) + (x - 2). Simplifying the equation, we get: x - 4 = -x + 2 + x - 2 x - 4 = 0 x = 4

Therefore, the solutions to the equation x - 4 = |x - 2| + (x - 2) are x = 1 and x = 4.

Answer

The solutions to the equation x - 4 = |x - 2| + (x - 2) are x = 1 and x = 4.