Objectives
Students should be able to identify order-preserving moves while solving inequalities in one variable and justify the solution for a linear inequality in one variable.
Vocabulary
inequality
variable
equation
solution-preserving moves
Students develop a sense of “order- and solution-preserving” moves that can be applied to inequalities and how these moves relate to the solution set for an inequality.
Students will encounter the fact that multiplying both sides of an inequality by a negative number does not preserve order.
What are all the possible whole numbers that make 8-___>3 true?
a. 0, 1, 2, 3, 4, 5
b. 0, 1, 2, 3, 4
c. 0, 1, 2
d. 5
Answer: b
Finding the solution to an inequality in one variable involves four ideas:
1. The smaller of two number is to the left of the larger;
2. if one number is less than another, \(a < b\), then some positive \(c\) added to \(a\) will equal \(b\) \((a+c = b)\);
3. the point of equality (boundary point) divides a set of values into those greater than and those less than that point; and
4. some operations on both sides of an inequality preserve order and some do not (in particular, multiplying or dividing by a non-zero number).
Students reason about order-preserving and solution- preserving moves while using interactive visuals on a number line.
Encourage students to think about the ways they learned to solve equations that apply similarly to solving inequalities.
