how do you solve this equation:
w+3.14=0.5(2w+6.38)
after you expand the right side, you get
w+3.14 = w + 3.19
and then 3.14 = 3.19 which is a FALSE statement.
Therefore there is no solution to your equation.
If after simplifying you end up with a FALSE statement, there is no solution.
If after simplifying you end up with a TRUE statement, there would be an infinite number of solutions, that is, anything you put in for the variable would satisfy the equation. The equation would then be what is called an "identity"