Solutions of Inequalities
In this lesson, students consider situations where there might be more than one condition. Students have already learned “solution to an equation” to mean a value of the variable that makes the equation true. Here, they learn a similar definition about inequalities: a solution to an inequality is a value of the variable that makes the inequality true. But while the equations students solved in the last unit generally had one solution, the inequalities they solve in this unit have many, sometimes infinitely many, solutions.
Constraints in real-world situations reduce the range of possible solutions. Students reason abstractly by using inequalities or graphs of inequalities to represent those situations and interpreting the solutions, (MP2). Students think carefully about whether to include boundary values as solutions of inequalities in various contexts.
- Draw and label a number line diagram to represent the solutions to an inequality.
- Recognize and explain (orally and in writing) that an inequality may have infinitely many solutions.
- Use substitution to justify (orally) whether a given value is a “solution” to a given inequality.
Let’s think about the solutions to inequalities.
The included blackline master is for the optional activity, “What Number Am I?” Print and cut up slips from the blackline master. Prepare 1 set of inequalities and 1 set of numbers for each group of 4 students. Colored pencils are only needed for an “Are You Ready for More” problem.
- I can determine if a particular number is a solution to an inequality.
- I can explain what it means for a number to be a solution to an inequality.
- I can graph the solutions to an inequality on a number line.
solution to an inequality
A solution to an inequality is a number that can be used in place of the variable to make the inequality true.
For example, 5 is a solution to the inequality \(c<10\), because it is true that \(5<10\). Some other solutions to this inequality are 9.9, 0, and -4.
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