(x-8)+4x=2( )+x how to make this infinitely many solutions?

To make this equation have infinitely many solutions, we want to end up with the equation x=x. With this equation, no matter what number we plug in for x, it will be a solution since it will equal itself.

-(x-8)+4x=2()+x
-x+8+4x=2()+x
-2x+8+4x=2()
2x+8=2()
x+4=()

Therefore if we plug x+4 into the equation we will find our equation with infinitely many solutions.

-(x-8)+4x=2(x+4)+x

We can check our solution:
-(x-8)+4x=2(x+4)+x
-x+8+4x=2x+8+x
3x+8=3x+8

Since the right and left side of the equation our equal, we know our solution works.