An algebra problem by Arpan Ray

$\begin{aligned} \left( \dfrac{2x+2}{2} \right) - x & = & \left( \dfrac{2(x+1)}{2} \right) - x \\ & = & x+1-x \\ & = & \boxed{1} = y \end{aligned}$

It is an equation where $x$ can have any positive value. The different values of $x$ will not change the value of $y$ . It will remain 1 only. Example:-

{If $x$ = 6}

= [ $\frac{2*6+2}{2}$ ] - $6$

= [ $\frac{12+2}{2}$ ] - $6$

= [ $\frac{14}{2}$ ] - $6$

= $7 - 6$ = $1$

{If $x$ = 7}

= [ $\frac{2*7+2}{2}$ ] - $7$

= [ $\frac{14+2}{2}$ ] - $7$

= [ $\frac{16}{2}$ ] - $7$

= $8 - 7$ = $1$

So, $y = 1$