In this lesson, students practice solving inequalities without any context to help support their number reasoning. First, students solve the corresponding equation to identify the boundary point between values that will make the inequality true and values that will make it false. Then students test various values above or below the boundary point to determine which values satisfy the original inequality. They use these test values to reason about the direction of the inequality symbol for the solution. Eventually, students see that they only need to test one value either above or below the boundary point to be able to determine the solution to the inequality. As students generalize a process for determining the solution to an inequality, they make use of repeated reasoning (MP8).

It is important to understand that the goal is not to have students learn and practice an algorithm for solving inequalities like “whenever you multiply or divide by a negative, flip the inequality.” Instead, students should understand that solving a related equation tells them the lower or upper bound of an inequality, and testing some values that are above or below the boundary number reveals which values make the inequality true. This way of reasoning about inequalities will serve students well long into their future studies, whereas students are very likely to forget a procedure memorized for a special case.