x=1+(1/2)x

x=1+(1/2)x

$$\\
\begin{array}{rcl}
x &=& 1+\frac{1}{2}x \quad | \quad -\frac{1}{2}x \\
x - \frac{1}{2}x &=& 1 \quad | \quad \times 2 \\
2x-x &=& 2 \quad | \quad +1\\
x &=& 2
\end{array}
$\\$
\small{\text{
Proof:
$
\begin{array}{rcl}
2 &=& 1 + \frac{1}{2}*2 \\
2 &=& 2
\end{array}
$
}}$$