Solve:
$\{2\ -\ ( 2\ \div \ 2) \ +\ 2( 2\ -\ 2\ -\ 2)\} \ +\ ( 2\ \div \ 2) \ \times \ 2$

Given: $\{2\ -\ ( 2\ \div \ 2) \ +\ 2( 2\ -\ 2\ -\ 2)\} \ +\ ( 2\ \div \ 2) \ \times \ 2$.

To find: Here we have to find the value of the given expression $\{2\ -\ ( 2\ \div \ 2) \ +\ 2( 2\ -\ 2\ -\ 2)\} \ +\ ( 2\ \div \ 2) \ \times \ 2$.

Solution:

Using BODMAS rule to solve this problem;

$\{2\ -\ ( 2\ \div \ 2) \ +\ 2( 2\ -\ 2\ -\ 2)\} \ +\ ( 2\ \div \ 2) \ \times \ 2$

$=\ \left\{2\ -\ \left(\frac{2}{2}\right) \ +\ 2( -2)\right\} \ +\ \left(\frac{2}{2}\right) \ \times \ 2$

$=\ \{2\ -\ 1\ -\ 4\} \ +\ ( 1) \ \times \ 2$

$=\ \{1\ -\ 4\} \ +\ 2$

$=\ -3\ +\ 2$

$=\ \mathbf{-1}$

So, value of the given expression is -1.