To simplify equation, let's make arithmetic operations in the left side using the rules of brackets.

First calculate the expression in straight brackets

    [3x - (8x+7)] = -5x - 7.

Now substitute -5x-7 instead of straight brackets and calculate expression in curly brackets

    {x - [-5x-7]} = 6x + 7.


Next, substitute 6x + 7 instead of curly brackets and calculate expression in the left side

    2x - (6x+7) = -4x - 7


So, the original equation takes the form

    -4x - 7 = 4x + 1.


Collect the terms with x on the right side; collect the constant terms on the left side

    -7 - 1 = 4x + 4x


Combine like terms

      -8   =   8x  


Find x

      x     =  (-8)/8 = -1.


ANSWER.  x = -1.


CHECK.   You may check it on your ow, by substituting x= -1 into the original equation.

         You will get the value of -3 in the left side and the same value -3 in the right side,
         confirming the answer.