No Solution

Not every equation has a solution. The equation $x+3 = x+5$ says that a number plus 3 equals the same number plus 5. No number can do that. Solve it anyway and see what happens. Subtract $x$ from both sides:

$$3 = 5$$

The $x$ terms cancel out, and what is left is a false statement. A false statement means the original equation is false for every value of $x$. The equation has no solution. Every step was correct. The answer is that no number works.

You cannot tell from the look of an equation whether it has a solution. The equation $2\left(x+1\right) = 2x+5$ looks ordinary. Distribute the left side to get $2x+2 = 2x+5$. Subtract $2x$ from both sides and you get $2 = 5$. Whenever the $x$ terms cancel out completely, look at the statement that is left. If it is false, the equation has no solution.