# 6.1: Inequalities Using Addition and Subtraction

## Learning Objectives

At the end of this lesson, students will be able to:

- Write and graph inequalities with one variable on a number line.
- Solve an inequality using addition.
- Solve an inequality using subtraction.

## Vocabulary

Terms introduced in this lesson:

- inequality
- interval, interval of values

## Teaching Strategies and Tips

Use Examples 1 and 2 to introduce the number line as a way to graph the solution set to an inequality.

- Point out that the solution sets in Examples 1 and 2 represent all numbers which make the statements true. The solution to a linear equation is a
*number*; the solution to an inequality, an*interval of (infinite) numbers.* - Remind students that an open circle is used for inequalities containing a or symbol and a closed circle for inequalities containing a or symbol.

Additional Examples:

*Graph the following inequalities on the number line.*

a.

b.

c.

d.

*Write the inequality that is represented by each graph.*

a.

b.

c.

d.

In Example 3, students learn to identify inequalities in sentences. The following chart might be useful for those students having difficulty choosing the correct symbol.

Additional Examples:

*Write each statement as an inequality and graph it on the number line.*

- You were told not to spend any more than at the arcade.
- Fewer than tickets are available for sale to the musical performance.
- You must be taller than to get on this ride.
- The FDA allows for or more insect fragments per of peanut butter.

Use Examples 4 and 5 to show students how to isolate variables in inequalities using addition and subtraction.

- Point out that solving inequalities is analogous to solving equations.
- The exception occurs when multiplying or dividing by a negative number. See the lesson
*Inequalities Using Multiplication and Division.*

## Error Troubleshooting

General Tip: Suggest to students having difficulty with inequalities that the inequality opens to the larger number.

- is read as “ is less than ” or “ is greater than ,” depending on the perspective.
- In a statement such as , suggest that students take the point of view of the unknown: “ is greater than ” or “all real numbers greater than ” instead of “ is less than ”.

In Example 5d, remind students of *mixed number form* and that .