# Expressions and Equations / Linear Inequalities in One Variable

Activity 8 of 18
In this lesson students focus on inequalities and methods of solving them, building on the concept of solution- and order-preserving moves in the context of an inequality.

## Planning and Resources

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

Standard:

## Lesson Snapshot

#### Understanding

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.

### What to look for

Students will encounter the fact that multiplying both sides of an inequality by a negative number does not preserve order.

### Sample Assessment

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

#### The Big Idea

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).

### What are the students doing?

Students reason about order-preserving and solution- preserving moves while using interactive visuals on a number line.

### What is the teacher doing?

Encourage students to think about the ways they learned to solve equations that apply similarly to solving inequalities.