In order to have an equation with no solution, the variable x should not appear in the equation and the final sentence must be false.
So, using the variable 'y' to represent the missing number and simplifying the equation, we have:
[tex]\begin{gathered} -4(-x+8)=-3(2x+7)+yx+9 \\ 4x-32=-6x-21+9+yx \\ 4x+6x-yx=32-21+9 \\ 10x-yx=20 \\ (10-y)x=20 \end{gathered}[/tex]
Since we want the variable x to disappear (this way we will have 0 = 20, which is false), we need the coefficient (10 - y) to be zero:
[tex]\begin{gathered} 10-y=0 \\ y=10 \end{gathered}[/tex]
So the missing number is 10.
