Verified Answer :

dln

\(|x-1|= \frac{x}{2} \\ \\ x-1=- \frac{x}{2} \\ 2x-2=-x \\ 3x-2=0 \\ 3x=2 \\ x= \frac{2}{3} \\ \\ x-1= \frac{x}{2} \\ 2x-2=x \\ x-2=0 \\ x=2 \\ \\ \boxed{x= \frac{2}{3}\ and\ 2 }\)

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