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# Chapter1.9

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### Chapter1.9

1. 1. Warm Up Lesson Presentation California Standards Preview
2. 2. Warm Up Add or subtract. 1. –6 + (–5) 2. 4 – (–3) 3. –2 + 11 Multiply or divide. 4. –5(–4) 5. 6. 7(–8) – 11 7 9 20 – 6 – 56 18 – 3
3. 3. AF4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results. Also covered: AF1.1 California Standards
4. 4. Two-step equations contain two operations. For example, the equation 6 x  2 = 10 contains multiplication and subtraction. 6 x  2 = 10 Subtraction Multiplication
5. 5. Translate the sentence into an equation. 17 less than the quotient of a number x and 2 is 21. Additional Example 1A: Translating Sentences into Two-Step Equations 17 less than the quotient of a number x and 2 is 21. ( x ÷ 2) – 17 = 21 x 2  17 = 21
6. 6. Translate the sentence into an equation. Twice a number m increased by – 4 is 0. Additional Example 1B: Translating Sentences into Two-Step Equations Twice a number m increased by –4 is 0. 2 ● m + (–4) = 0 2 m + (–4) = 0
7. 7. Translate the sentence into an equation. 7 more than the product of 3 and a number t is 21. Check It Out! Example 1A 7 more than the product of 3 and a number t is 16. 3 ● t + 7 = 16 3 t + 7 = 16
8. 8. Translate the sentence into an equation. 3 less than the quotient of a number x and 4 is 7. Check It Out! Example 1B 3 less than the quotient of a number x and 4 is 7. ( x ÷ 4) – 3 = 7 x 4  3 = 7
9. 9. Solve 3 x + 4 = –11. Additional Example 2A: Solving Two-Step Equations Using Division 3 x + 4 = –11 Step 1: Note that x is multiplied by 3. Then 4 is added. Work backward: Since 4 is added to 3x, subtract 4 from both sides. – 4 – 4 3 x = –15 Step 2: 3 x = –15 3 3 x = –5 Since x is multiplied by 3, divide both sides by 3 to undo the multiplication.
10. 10. Solve 8 = –5 y – 2. Additional Example 2B: Solving Two-Step Equations Using Division 8 = –5 y – 2 Since 2 is subtracted from –5y, add 2 to both sides to undo the subtraction. + 2 + 2 10 = –5 y 10 = –5 y – 5 – 5 – 2 = y or Since y is multiplied by –5, divide both sides by –5 to undo the multiplication. y = –2
11. 11. Solve 7 x + 1 = –13. Check It Out! Example 2A 7 x + 1 = –13 Step 1: Note that x is multiplied by 7. Then 1 is added. Work backward: Since 1 is added to 7x, subtract 1 from both sides. – 1 – 1 7 x = –14 Step 2: 7 x = –14 7 7 x = –2 Since x is multiplied by 7, divide both sides by 7 to undo the multiplication.
12. 12. Solve 12 = –5 y – 3. Check It Out! Example 2B 12 = –5 y – 3 Since 3 is subtracted from –5y, add 3 to both sides to undo the subtraction. + 3 + 3 15 = –5 y 15 = –5 y – 5 – 5 – 3 = y or Since y is multiplied by –5, divide both sides by –5 to undo the multiplication. y = –3
13. 13. Solve 4 + = 9. Additional Example 3A: Solving Two-Step Equations Using Multiplication Step 1: – 4 – 4 Step 2: m = 35 Since m is divided by 7, multiply both sides by 7 to undo the division. m 7 4 + = 9 m 7 =  5 m 7 Note that m is divided by 7. Then 4 is added. Work backward: Since 4 is added to , subtract 4 from both sides. m 7 (7) = 5 (7) m 7
14. 14. Solve 14 = – 3. Additional Example 3B: Solving Two-Step Equations Using Multiplication Step 1: + 3 + 3 Step 2: 34 = z z is divided by 2, multiply both sides by 2 to undo the division. z 2 14 = – 3 z 1 2 17 = z 2 Since 3 is subtracted from t , add 3 to both sides to undo the subtraction. z 2 (2) 17 = (2) z 2
15. 15. Solve 2 + = 9. Check It Out! Example 3A Step 1: – 2 – 2 Step 2: k = 42 Since k is divided by 6, multiply both sides by 6 to undo the division. k 6 2 + = 9 k 6 =  7 k 6 Note that k is divided by 6. Then 2 is added. Work backward. Since 2 is added to , subtract 2 from both sides. k 6 (6) = 7 (6) k 6
16. 16. Solve 10 = – 2. Check It Out! Example 3B Step 1: + 2 + 2 Step 2: 48 = p p is divided by 4, multiply both sides by 4 to undo the division. p 4 10 = – 2 p 1 4 12 = p 4 Since 2 is subtracted from t , add 2 to both sides to undo the subtraction. p 4 (4) 12 = (4) p 4
17. 17. Donna buys a portable DVD player that costs \$120. She also buys several DVDs that cost \$14 each. She spends a total of \$204. How many DVDs does she buy? Additional Example 4: Consumer Math Application Let d represent the number of DVDs that Donna buys. That means Donna can spend \$14 d plus the cost of the DVD player. cost of DVD player cost of DVDs total cost + = \$120 14 d \$204 + =
18. 18. Donna buys a portable DVD player that costs \$120. She also buys several DVDs that cost \$14 each. She spends a total of \$204. How many DVDs does she buy? Additional Example 4 Continued 120 + 14 d = 204 14 d = 84 d = 6 Donna purchased 6 DVDs. \$120 14 d \$204 + = – 120 – 120 14 d = 84 14 14
19. 19. John buys an MP3 player that costs \$249. He also buys several songs that cost \$0.99 each. He spends a total of \$277.71. How many songs does he buy? Check It Out! Example 4 Let s represent the number of songs that John buys. That means John can spend \$0.99 s plus the cost of the MP3 player. cost of MP3 player cost of songs total cost + = \$249 0.99 s \$277.71 + =
20. 20. 249 + 0.99 s = 277.71 0.99 s = 28.71 s = 29 John purchased 29 songs. John buys an MP3 player that costs \$249. He also buys several songs that cost \$0.99 each. He spends a total of \$277.71. How many songs does he buy? Check It Out! Example 4 Continued – 249 – 249 \$249 0.99 s \$277.71 + = 0.99 s = 28.71 0.99 0.99
21. 21. Lesson Quiz Translate the sentence into an equation. 1. The product of –3 and a number c , plus 14, is –7. Solve. 2. 17 = 2 x – 3 3. –4 m + 3 = 15 4. – 5 = 1 5. 2 = 3 – – 3 c + 14 = –7 12 4 10 – 3 6. A discount movie pass costs \$14. With the pass, movie tickets cost \$6 each. Fern spent a total of \$68 on the pass and movie tickets. How many movies did he see? 9 w 2 x 4