This student guide discusses how to set up and solve word problems involving inequalities.

In this lesson, students understand that an inequality is a statement that one expression is less than (or equal to) or greater than (or equal to) another expression, such as 2x + 3 < 5 or 3x + 50 ≥ 100.
Students interpret a solution to an inequality as a number that makes the inequality true when substituted for the variable.
Students convert arithmetic inequalities into a new inequality with variables (e.g., 2 x 6 + 3 > 12 to 2m + 3 > 12 and give a solution; for example, m = 6, to the new inequality. They check to see if different values of the variable make an inequality true or false.

In this lesson, students solve word problems leading to inequalities that compare px + q and r, where p, q, and r are specific rational numbers. Students interpret the solutions in the context of the problem.