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Solving Linear Equations with Models and Algebra

Learn how to solve linear equations using models and algebraic methods. Practice solving equations involving fractions and distribution. Also, explore word problems and challenge questions.

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Solving Linear Equations with Models and Algebra

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  1. Chapter 6 Linear Equations and Graphing

  2. Write Down Any Number Add it to the number that comes after it Add 9 Divide by 2 Subtract your original number 5?!?!

  3. 6.1 Solving Equations Using Models

  4. INVESTIGATE

  5. Goal for Linear Equations =

  6. = 1 Using Models Tiles - Make zero pairs = -1 = -x = x 9 - x = 4 + 3 Goal X = ____

  7. Using Models 2) Balance the Scale! 9 - x = 4 + 3 Goal X = ____ = 1 = -1 = -x = x

  8. Example 1. x 42 x x

  9. Example 2. 13

  10. Example 3. Solve using whichever MODEL you choose. Danielle's Bikes rents bikes for $10.54 plus $4.98 hour. Ben paid $20.50 to rent a bike. For how many hours did he rent the bike?

  11. Practice Pages 324-326 #6* 7a*b* 12 13ab

  12. 6.2 Solving Equations Using Algebra!!

  13. INVESTIGATE Jen doesn't have enough hot dogs for all of her friends. She says that she needs twice as many, plus 5 more to feed everyone. She has 33 people total at her party. What is our variable? What is our total? What is our equation Solve! **Think about our balance scales…What can we do to the numbers to meet our goal of numbers on one side and variables on the other?

  14. Order of Operations BEDMAS…. When solving for variables, you do the opposite • SAMDEB

  15. Isolation of the variable! 1 step equations Example 1. x + 4 = 7 Example 2. -3 + x = -13

  16. Example 3. -2x = -48 Example 4. -3x = -3 Verify your answer.

  17. 2 Step Equations! 1. Opposite order of BEDMAS 2. Isolate the variable "What we do to one side we must do to the other!" Example 5. 2y + 8 = -16 Example 6. -2y - 2 = 11

  18. Example 7. The Grade 8 students had a dinner. They paid a flat rate 
of $125 for the use of the hall, plus $13 for each student 
who attended. The total cost of the dinner was $944. How many students attended the dinner? What is our variable? What is our total? What is our equation? Solve.

  19. Exit Slip Create a 2-step word problem and an equation to match each. This problem must contain a fraction. Switch with a partner, solve, and hand in!

  20. Practice Pages 331- 332 6a*c* 7b*c 8a*d 9 11cf 12e

  21. Section 6.3 Solving Equations Involving Fractions

  22. ReviewQuestions -23= 5p - 27

  23. Example 1. x = 3 Algebra with Fractions 4 x

  24. Example 2. Practice, Practice, Practice! 4h = -24 =

  25. Example 3. 2 6 - x = 12 3 =

  26. Solve! Example 4. 2p + 4 = 8 SAMDEB! *Subtraction and Addition FIRST!

  27. Check your solution! Example 5. 6 = -8 -2d

  28. Example 6. -6y + 7 = 73

  29. Example 7. 28 = z - 8 9

  30. Example 8. -24 + w = -29 5

  31. Word Problems Example 9. Halfa number plus5 is 11. What is the number?

  32. Word problems Example 10. Jane spent $42 for shoes.  This was $14 less than twice what she spent for a blouse.  How much was the blouse?

  33. Practice Pages 336 - 337 3b* 4d* 6* 7c*d 8bd 10 13b

  34. Challenge Questions Remember to "gather like terms" 2 + 3x - 6 + x = 4 -2 + 3x - 7 = 3

  35. 6.4 Distribution

  36. Review Question

  37. DistributiveProperty 4(x+ 7) a (b +c) = ab + ac

  38. 4(x+ 7) 4 groups of (x + 7) 4 groups of x and 4 groups of 7 They give us the same amount!

  39. Why does this work??? + b c a ab ac = ab + ac Remember**Area = l x w

  40. Distribute Expand Example 1. 5 (1 + x) Example 4. 3(5 + 4 +2y) Example 2. -(7 - x) Example 5. (4x +12) -1 4 Example 3. x(3+ 6)

  41. Example 6. 2 (8y - f + 3d)

  42. Example 7. Six times the difference of 2a and b, is increased by 4b Example 8. Two times the sum of x squared and y squared, increased by three times the sum of x squared and y squared

  43. Practice Pages 342 - 343 7d*e*i* 8b*g*j* 9 12e*fh 19def

  44. 6.5 Solving Equations Using Distribution

  45. Steps for Solving Equations 1.Simplify both sides! - distribution - gather "like" terms: add the opposite 2. Isolate for your variable - SAMDEB - Inverse operations

  46. 6(r+2)=16 Example 1. 9 = 2(x+3)

  47. Example 2. Example 3. -7( -3)=49 -3( +6) = 18

  48. Example 4. Challenge Question 4(9v - 2) = 2 (v+30)

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