How many solutions does 3 - 2x = 5-x+ 3 + 4x have?

One solution

Step-by-step explanation:

If you put the two equations on a graphing calculator you would see that there are only 1 point that has intersected.  For a more written answer, you would combine -x and 4x to get 3x and 5 and 3 to get 8.

From there on out, you would then have this equation 3 - 2x = 8 + 3x.  Add 2x both sides to get 3 = 8 + 5x, then subtract 8 both sides to get -5 = 5x.  Divide both sides to get x = -1.  This is the only known solution that I know of.