In this lesson, students revisit inequalities of the form or , and are introduced to the symbols to show “greater than or equal to,” and to show “less than or equal to.” Students begin by finding values that are a solution to a given inequality by determining if the value makes the inequality true. Next, they consider how to represent a context involving the phrase “at least” using algebraic notation and graphically on a number line. The necessity for both an equation and an inequality leads to the introduction of the symbols and . Lastly, students use substitution to determine whether given values make different inequalities true or false. Students must attend to precision when they specify the meaning of the inequality symbols and explain which values make each inequality true or false (MP6).
Comprehend the terms “less than or equal to” and “greater than or equal to” (in spoken and written language) and the symbols ≤ and ≥ (in written language).
Recognize that more than one value for a variable makes the same inequality true.
Use substitution to determine whether a given value for a variable makes an inequality true, and justify (orally) the answer.
Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
Solve word problems leading to inequalities of the form or , where , , and are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. \$