Introduction

In Lesson 2, you will be solving linear inequalities. You will use many of the skills you learned previously when solving equations. You will also graph solutions on a number line and solve compound inequalities. Study this chapter carefully. Take your time and practice. Ask questions if you get stuck.

Let’s begin.

Lesson Objectives

After completing this lesson, you should be able to:

• solve linear inequalities in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides.

Materials Needed

• Textbook: Big Ideas Math, Algebra 1
• Spiral notebook for notes
• Graphing calculator

How to Proceed

1. Read the Introduction and Objectives for this lesson. They will give you an idea of the major concepts you need to watch for as you read, as well as the kinds of skills you will be expected to have at the end of the lesson.
   
   
2. Survey pages 42-85 in your textbook. (Skim and/or look at the title, the introduction, the headings and subheadings, the graphics, and the important terms. The Chapter Review on pages 80-82 is a good place to see an overview of what you’ll be learning in Lesson Two.)
   
   
3. Read the assigned pages in your textbook for each section of this lesson. The assigned textbook readings are given at the beginning of each Section Summary.
   
   
4. Take notes on the assigned pages for each section. Pay attention to the list of key words in each section. The key words are important and should be remembered for future reference.
   
   
5. Read the Section Summaries on the course homepage. They will help you to understand what you read in the textbook. Read and study all examples given in the textbook.
   
   
6. Complete the Section Assignments neatly on paper to be scanned and saved as a PDF (see "Textbooks and Materials" in the Course Introduction). Show every step and box your answers as shown in the Sample Lesson Submission in the Resources section of this course. When you have completed all of the assignments, save them as a single PDF and upload your work using the Lesson Two: Assignment Upload.
   
   
7. Review your notes briefly every day until you complete the course. After you have finished this lesson, you may proceed to Lesson Three.

Before You Begin

Before you begin this chapter, look through the whole chapter to become acquainted with what will be covered. Remember that each chapter has two sections labeled "What Did You Learn?". This part of the book lists the core vocabulary and core concepts. Make sure that you have all of the core vocabulary and core concepts written in your notes and defined. You may also want to add some examples.

Now look at pages 43 and 44. Work through Maintaining Mathematical Proficiency and Mathematical Thinking. This will serve as a review of some skills and topics that you should know and will also need for this chapter. Remember your rules for operations with integers.

Remember that positive numbers are greater than 0 and are to the right of 0 on a number line. Negative numbers are less than 0 and are to the left of 0 on a number line.

The absolute value of a number is the distance between the number and 0 on a number line. Graph each pair of integers on a number line. On a horizontal number line, the number on the right is the greater number.

Answers to Maintaining Mathematical Proficiency (page 43)

Check your answers in the Selected Answers section of your textbook, beginning on page A1.

Answers to Monitoring Progress (page 44)

On page 44, you are learning how to graph an inequality using a graphing calculator. You may have to use your User’s Guide when learning how you graph on your calculator.

Answers are:

1. x < –4
2. x > 3
3. x ≥ –2