In this lesson, students encounter equations that have no solutions and equations for which every number is a solution. In the first case, when students try to solve the equation, they end up with a false statement like . In the second case, they end up with a statement that is always true, such as . In preparation for predicting the number of solutions from the structure of an equation, students add missing terms in three different ways to make them have no solution, one solution, or infinitely many solutions.