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Chapter 3 Multi-Step Equations and Inequalities

Chapter 3 Multi-Step Equations and Inequalities. Chapter Prerequisite Skills. Chapter Prerequisite Skills. 1. Explain what an expression is and what an equation is. Then give one example.

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Chapter 3 Multi-Step Equations and Inequalities

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  1. Chapter 3Multi-Step EquationsandInequalities Chapter Prerequisite Skills

  2. Chapter Prerequisite Skills 1. Explain what an expression is and what an equation is. Then give one example. An expression can be a variable expression or a numerical expression. It is not equal or compared to anything. 2x + 7 or 28 – 7 An equation is a mathematical sentence comparing two expressions. 2x + 7 = 28 – 7 Use the distributive property to write and equivalent variable expression. 2.9(x – 4) 9x - 36 3.8(z – 7) 8z – 56 4.-6(-m + 12) 6m – 72 5.-10(n – 5) -10n + 50

  3. Chapter Prerequisite Skills Simplify the Expression. 6.c + 4 – c 4 7.9b – 12b + 3 -3b + 3 8.4(a + 2) + a 5a + 8 9.2(2d+ 5 + d) 6d +10 Solve the equation. Check the solution. 10.x + 13 = 7 -6 11.h ÷ 6 = -8 -48 12.q – 9.6 = 2 11.6 13.65 = -13b -5

  4. Lesson 3.1Solving Two-Step Equations Skill Check Lesson Presentation Lesson Quiz

  5. Skill Check 1. -44 – 88 = -132 2. -77 + 37 = -40 3. -270 ÷ -4 = 67.5 4. 765 • (1 ÷ 765) = 1

  6. Writing Variable Expressions You can solve a real-world problem by creating a verbal model and using it to write a variable expression. A verbal modeldescribes a problem using words as labels and using math symbols to relate the words. The table shows common words and phrases that indicate mathematical operations.

  7. Study Strategy When you solve an equation show every step when solving, because these steps are important for diagnosing errors. For example: 3x + 7 = -5 Subtract 7 from both sides: -7 + 3x + 7 = -5 – 7 Simplify:3x = -12 Divide each side by 3: 3x ÷ 3 = -12 ÷ 3 Simplify:x = -4

  8. 1 EXAMPLE Using Subtraction and Division to Solve Solve. a. 8x + 7 = 47 b. 1 = 2r + 9 c. 2 = 6h + 20 SOLUTION b. 1 = 2r + 9 c. 2 = 6h + 20 a. 8x + 7 = 47 -7 + 8x + 7 = 47 - 7 -9 + 1 = 2r + 9 – 9 -20 + 2 = 6h + 20 – 20 8x = 40 -8 = 2r -18 = 6h 8x/ 8 = 40/ 8 -8/2 = 2r/2 -18/6 = 6h/6 x = 5 r = -4 h = -3

  9. 2 EXAMPLE Using Addition and Multiplication to Solve Solve. a. y/4– 2 = 1 b.2 = d/5 - 1 c. 12 = f/2 – 8 SOLUTION b. 2 = d/5 - 1 c. 12 = f/2 – 8 a. y/4 – 2 = 1 2 + y/4 – 2 = 1 + 2 1 + 2 = d/5 – 1 + 1 8 + 12 = f/2 – 8 + 8 y/4 = 3 3 = d/5 20 = f/2 4(y/4) = (3)4 5(3) = (d/5)5 2(20) = (f/2)2 y = 12 d = 15 f = 40

  10. 3 EXAMPLE Solving an Equation with Negative Coefficients Solve. a. 9 – 6a = 45 b. 6 – 2m = 8 c. -2 = 5 – n SOLUTION b.6 – 2m = 8 c. -2 = 5 – n a. 9 – 6a = 45 -9 + 9 – 6a = 45 – 9 -6 + 6 – 2m = 8 – 6 -5 – 2 = 5 – n – 5 – 6a = 36 – 2m = 2 -7 = -n – 6a/-6 = 36/-6 – 2m/-2 = 2/-2 -7/-1 = -n/-1 a = -6 m = -1 n = 7

  11. 4 EXAMPLE Writing and Solving a Two-Step Equation MotorcycleWilliammakes a down payment of 1,100,000 won on a motorcycle costing 2,300,000 won. If no interest is charged, how many monthly payments of 150,000 won must he make until he has finished paying for the motorcycle? Let p represent the number of monthly payments. Write a verbal model. SOLUTION 1100000 + 150000 • p = 2300000 – 1100000 + 1100000 + 150000p = 2300000 - 1100000 150000p = 1200000 150000p/150000 = 1200000/150000 p = 8 ANSWER Williammust make 8 monthly payments of 150000 won.

  12. Lesson Quiz Solve the equation. 1. 9b + 8 = 80 b = 8 2.z/7- 5 = -3 z = 14 3. -10 = 20 – 6c c = 5 4. 11 – b/6 = 23 b = -72 5. ChallengeSolve (8 + k)/5 = 3 k = 7

  13. Closure • 1.) Explain how you solve the equation • 11 – 4p = -1? • 2.) Asia girl has lived one fourth of her life in S.Korea, one fifth of her life in Thailand, one third of her life in China, and she has been living in Japan for the past 13 years. How old is Asia girl? Asia girlis 60 years old. 

  14. Lesson 3.1 Homework: • pp.122-124 Exs. (1, 20, 22, 24, 26, 28, 30, 32, 34, 35abc, 45, 46) • Challenge/Bonus 36

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