Question

| x-3| = | 2x-3|

Answer 1

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

\(\Rightarrow\left[{}\begin{matrix}x-3=2x-3\\x-3=-\left(2x-3\right)\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}3x=0\\3x=6\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\x=2\end{matrix}\right.\)

Answer 2

TH1: x ≥ 3, ta có:

x - 3 = 2x - 3

2x - x = -3 + 3

x = 0 (loại)

3 - x = 2x - 3

2x + x = 3 + 3

3x = 6

x = 6 : 3

x = 2 (nhận)

3 - x = 3 - 2x

-x + 2x = 3 - 3

x = 0 (nhận)

Vậy x = 0; x = 2