\(\left(x-1\right):\frac{1}{2}=\frac{1}{2}+1\frac{1}{2}\)
\(\Rightarrow\left(x-1\right).2=1+1\)
\(\Rightarrow\left(x-1\right).2=2\)
\(\Rightarrow\left(x-1\right)=2:2\)
\(\Rightarrow x-1=1\)
\(\Rightarrow x=1+1\)
\(\Rightarrow x=2\)
\(\left(x-1\right):\frac{1}{2}=\frac{1}{2}+\frac{3}{2}\)
\(\left(x-1\right):\frac{1}{2}=\frac{4}{2}\)
\(\left(x-1\right):\frac{1}{2}=2\)
\(x-1\) \(=2\)x \(\frac{1}{2}\)
\(x-1\) \(=1\)
\(x\) \(=1+1\)
\(x\) \(=2.\)