1. Warm Up Evaluate each expression for the given values of the variables. 1. 2x – 3y for x = 17 and y = 6 2. 5(x + 3) + 4y for x = 3 and y = 2 3. 6.9(x – 2.7) + 7.1 for x = 5.1 4. 5x – 4y for x = 0.3 and y = 0.2 16 38 23.66 1-3 Integers and Absolute Value Course 3 0.7

2. Learn to compare and order integers and to evaluate expressions containing absolute value. 1-3 Integers and Absolute Value Course 3 Vocabulary integer opposite additive inverse Absolute value

3. Course 3 Integers are the set of whole numbers and their opposites. On a number line, opposites, or additive inverses, are numbers that are the same distance from 0, but on opposite sides of 0 on the number line. 1-3 Integers and Absolute Value Course 3 Numbers on a number line increase in value as you move from left to right. Remember! –5 –4 –3 –2 –1 0 1 2 3 4 5 increase decrease

4. Use, or = to compare the scores. Additional Example 1A: Sports Application A.Aaron’s score is 4, and Felicity’s score is –1. Place the scores on the number line. –1 < 4 1-3 Integers and Absolute Value Course 3 –5 –4 –3 –2 –1 0 1 2 3 4 5 –1 is to the left of 4.

5. Use, or = to compare the scores. Check It Out: Additional Example 1A B. Naomi’s score is –2, and Terrence’s score is –3. Place the scores on the number line. –3 < –2 1-3 Integers and Absolute Value Course 3 –5 –4 –3 –2 –1 0 1 2 3 4 5 –3 is to the left of –2.

6. Use, or = to compare the scores. Additional Example 1B: Sports Application C. List the golf scores in order from the lowest to the highest. The scores are –4, 2, 5, and –3. Place the scores on the number line and read them from left to right. In order from the lowest score to the highest score, the scores are –4, –3, 2, and 5. 1-3 Integers and Absolute Value Course 3 –5 –4 –3 –2 –1 0 1 2 3 4 5

7. Use, or = to compare the scores. Check It Out: Additional Example 1B D. List the golfer’s scores in order from the lowest to the highest. The scores are –3, 1, 0, and –2. Place the scores on the number line and read them from left to right. In order from the lowest score to the highest score, they are –3, –2, 0, and 1. 1-3 Integers and Absolute Value Course 3 –5 –4 –3 –2 –1 0 1 2 3 4 5

8. E. Write the integers 8, –5, and 4 in order from least to greatest. Additional Example 2: Ordering Integers 8 > –5, 8 > 4, and –5 < 4 Compare each pair of integers. –5, 4, and 8. 1-3 Integers and Absolute Value Course 3 –5 is less than both 4 and 8.

9. F. Write the integers 7, –12, and 13 in order from least to greatest. Check It Out: Additional Example 2 13 > –12, 13 > 7, and –12 < 7 Compare each pair of integers. –12, 7, and 13. 1-3 Integers and Absolute Value Course 3 –12 is less than both 7 and 13.

10. Both 4 and –4 are 4 units from 0. 1-3 Integers and Absolute Value Course 3 –5 –4 –3 –2 –1 0 1 2 3 4 5 A number’s absolute value is its distance from 0 on a number line. Absolute value is always positive because distance is always positive. “The absolute value of –4” is written as –4. Additive inverses have the same absolute value. 4 units 4 units –4 = 4 = 4.

11. Find the additive inverse of each integer. Additional Example 3: Finding Additive Inverses A. 6 –6 B. –14 1-3 Integers and Absolute Value Course 3 –6 is the same distance from 0 as 6 is on the number line. 14 14 is the same distance from 0 as –14 is on the number line. C. 0.5 –0.5 –0.5 is the same distance from 0 as 0.5 is on the number line.

12. Find the additive inverse of each integer. Check It Out: Additional Example 3 A. 12 –12 B. –1.9 1-3 Integers and Absolute Value Course 3 –12 is the same distance from 0 as 12 is on the number line. 1.9 1.9 is the same distance from 0 as –1.9 is on the number line. C. 1 –1 –1 is the same distance from 0 as 1 is on the number line.

13. Evaluate each expression. Additional Example 4: Evaluating Absolute-Value Expressions A. –8 + –5 1-3 Integers and Absolute Value Course 3 –8 is 8 units from 0. 8 + 5 = 13 –8 = 8 –5 is 5 units from 0. –5 = 5 B. 5 – 6 –1 is 1 units from 0. –1 = 1

14. Evaluate each expression. Check It Out: Additional Example 4 C. –2 + -9 1-3 Integers and Absolute Value Course 3 –2 is 2 units from 0. 2 + 9 = 11 –2 = 2 –9 is 9 units from 0. –9 = 9 D. 1 – 1 0 is 0 units from 0. 0 = 0

15. Lesson Quiz Write the integers in order from least to greatest. 1. –17, –26, 23 2. 0, 5, –4 Evaluate each expression. 3. The sum of 3 and the additive inverse of –8 4. – –4 + –2 5. At the end of the course, your golf score was –2. Your friend’s score was 7. What is the difference between your scores? –26, –17, 23 –4, 0, 5 11 -2 9 1-3 Integers and Absolute Value Course 3