## Intermediate Algebra (6th Edition)

$x+4=x+5$
In order to write an equation in x that has no solution, we can write an equation where both sides have the same variable terms but different constant terms. In this case, the variable terms will cancel out and we will be left with differing constants on both sides, which tells us that the equation has no solution. For example, consider the equation $x+4=x+5$. To simplify, we can subtract x from both sides (in other words, we can cancel out the variable term). $4=5$, this statement is false. Therefore, we know that the equation has no solution.