|x - 1| + |1 - x| = 4 - x
Vì x - 1 và 1 - x là 2 số đối nhau
⇒ |x - 1| = |1 - x|
⇒ 2 . |x - 1| = 4 - x
⇒ |x - 1| = $\frac{4-x}{2}$
⇒ \(\left[ \begin{array}{l}x-1=\frac{4-x}{2}\\x-1=\frac{-(4-x)}{2}\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}2(x-1)=4-x\\2(x-1)=-(4 - x)\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}2x-2=4 - x\\2x-2=-4+x\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}2x+x=4+2\\2x-x=-4+2\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}3x=6\\x=-2\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}x=2\\x=-2\end{array} \right.\)
Vậy x ∈ {2; -2}
