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# Chapter 3 – Solving Linear Equations

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1. Chapter 3 – Solving Linear Equations Algebra 1 Fall 2013

2. What will we do in Chapter 3? • Solve linear equations using addition and subtraction • Use linear equations to solve real-life problems • Use multiplication and division to solve linear equations • Solve multi-step equations with variables on both sides of the equals sign • Problem solve with various equations • Learn how to use manipulate decimals in linear equations

3. 3.1 – Solving Equations Using Addition and Subtraction

4. Objectives • Solve linear equations using addition and subtraction • Use linear equations to solve a variety of real-life problems

5. What is an Equation? • Has an equal sign • Combination of numbers and variables • Complete thought with numbers and variables on left and right of the equal sign

6. Equation = Scale • Equations have two sides • Want to keep both sides equal

7. x = 2 “What value does x have?”

8. x + 3 = 5 We need x to have a value that will balance the scale!

9. What if Mental Math isn’t an Option? • We need a process to solve more difficult problems • We need to use inverse operations

10. Inverse Operations • Definition: • Examples: • Why do we use inverse operations? Operations that undo each other Addition and subtraction Multiplication and division To isolate the variable (get the variable by itself)

11. State the Inverse Operation • Add 7 • Subtract 3 • Add -11 • Subtract -2

12. Steps to Solving One-Step Equations • Simplify both sides of the equation • Isolate the variable (by using the inverse operation) • Find the solution • Check your solution

13. x - 5 = 16 Check

14. x - 5 = -13 Check

15. -8 = x – (-4) Check

16. x - 5 + 2 = -10 Check

17. Linear Equation • Definition: Equation in which the variable is raised to the first power and does not occur in a denominator inside a square root symbol, or inside absolute value symbols

18. Find the Linear Equations x + 5 = 9 x2 – 8 = 16 -4 + x = 7 – 3x 16 + 5 = (x/5) (2/x) + 1 = -10 | -17 + x | = 1 x3 + (-3) = 12 -6 = x

19. Writing Equations • You have x dollars and your friend pays you \$6 that he owed you. You now have \$14. How much money did you have before your friend paid you?

20. Writing Equations • A telephone pole extends 4 feet below the ground and 16 feet above the ground. What is the total length x of the telephone pole?

21. Equivalent Equations • Definition: Two equations that have the same solution 2 + x = 9 x + (-2) = 5 The equations are equivalent because the solution to both equations is x = 7.

22. Find the Equivalent Equations Draw an arrow from the equations on the left to their equivalent equations on the right. x + 1 = 9 x = -7 8 + x = 5 x + (-3) = -10 4 + (-7) = x 5 + x = 13

23. Tricky Equations | -6 | + x = 11 | 5 | + 7 = x x + 2 = 11 + 2 x – (-2) = 5 -x = -10

24. Reminders • 3.1-3.3 Quiz on Thursday, Sept. 12th • Homework: • P. 135 #’s 33-44 • P. 137 #’s 66-68

25. 3.2 – Solving Equations Using Multiplication and Division

26. 3.2 – Solving Equations Using Multiplication and Division • Objective: Solve one-step equations using multiplication and division.

27. State the inverse operation. This problem means -4 times x.

28. State the inverse operation. This problem means x divided by 5.

29. Solve the equation.

30. Solve the equation.

31. Solve the equation.

32. Solve the equation.

33. Solve the equation. This problem means (-2/3) times m equals 10.

34. REMEMBER! • Dividing by a fraction is the same as multiplying by the reciprocal.

35. Solve the equation.

36. Solve the equation.

37. Solve the equation.

38. Solve the equation.

39. Word Problems • You ate three of the eight slices of pizza and you paid \$3.30 as your share of the cost. How much did the whole pizza cost? Write an equation!

40. Word Problems • Each household receives about 676 pieces of junk mail per year. About how many pieces of junk mail does a household receive per week? Write an equation!

41. Reminders • 3.1-3.3 Quiz on Thursday, Sept. 12th • Homework: • P. 142 #’s 28-36, 49-50

42. 3.3 Solving Multi-Step Equations When solving equations you must balance both side. • Simplify both sides of the equation. • Do the opposite operation to both sides. • Addition/Subraction • Multiplication/Division • Check!

43. Example 1 Solving a Linear Equations ü Solve the equations.

44. Example 1 Solving a Linear Equations ü Solve the equations.

45. Example 2 Combining Like Terms First ü Solve the equations.

46. Example 3 Using the Distributive Property ü Solve the equations.

47. Example 4 Multiplying by a Reciprocal First ü Solve the equations.

48. Example 5 Real World: Solving Equations A body temperature of 95°F or lower may indicate the medical condition called hypothermia. What temperature in the Celsius scale may indicate hypothermia? Use the formula:

49. Reminders • 3.1-3.3 Quiz on Thursday, Sept. 12th • Homework: • P. 148-149 #’s 16-36 EVEN’S ONLY

50. Solving Equations with Variables on Both Sides 3.4 Objectives: • Solve equations with variables on both sides. • Solve equations with variables in the real world. Vocabulary: none