Solve for x and check your solutions
-3+2x=-x+6

-3 + 2x = -x + 6   Add x to both sides
-3 + 3x = 6          Add 3 to both sides
       3x = 9          Divide both sides by 3
         x = 3

  -3 + 2x = -x + 6   Plug in 3 for all of the x's
-3 + 2(3) = -3 + 6   Multiply 2 and 3
    -3 + 6 = -3 + 6   

Since both sides of the equation are the same you know that 3 made the equation equivalent.