Question

3+|x-1|=2(x-1)

Answer 1

3 + \(\left|x-1\right|\) = 2(x-1)

\(\Leftrightarrow\) \(\left|x-1\right|\)= 2x -5

+ Nếu x + 1 \(\ge\) 0 \(\Rightarrow\) x \(\ge\) -1 thì

\(x - 1 = 2x - 5 \)

\(\Leftrightarrow\)\( x - 2x = -5 + 1 \)

\(\Leftrightarrow\) \(- x = - 4 \)

\(\Leftrightarrow\)\( x = 4 \)(thõa mãn)

+ Nếu x - 1 < 0 \(\Rightarrow\) x < 1 thì:

\(- (x - 1) = 2x -5\)

\(\Leftrightarrow\)\(-x-2x=-5-1\)

\(\Leftrightarrow\)\(-3x = -6\)

\(\Leftrightarrow\) \(x = 2 \) (loại)

Vậy \( x = 4 \)