x=1+(1/2)x

x=1+(1/2)x

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