How many solutions does an equation have when the variable adds out and the final sentence is false?

Explanation:

When the variable adds out and the final sentence is false you have arrived to a contradiction, also called absurd, meaning that the starting equality was a wrong assumption that could never be true. Thus, the equation has no solutions.

An example of such situation is this equation:

To solve it, you use the subtraction property of the equalities: subtract both x and 3 from both sides:

The variable added out and the final sentences 0 = 6 is false. That means that none value of x satisfies the original equation and it has no solutions.