1. Linear Equations and Inequalities in One Variable What is an equation? =

2. Linear Equations and Inequalities in One Variable What is an equation?

3. Linear Equations and Inequalities in One Variable What is an equation?

4. Linear Equations and Inequalities in One Variable What is an equation?

5. Properties of Equality Reflexive Property a = a

6. Properties of Equality Symmetric Property If a = b then b = a

7. Properties of Equality Transitive Property If a = b and b = c then a = c

8. Properties of Equality Addition Property If a = b then a + c = b + c

9. Properties of Equality Subtraction Property If a = b then a - c = b - c

10. Properties of Equality Multiplication Property If a = b then ac = bc

11. Properties of Equality Division Property If a = b and c = 0 then a/c = b/c

12. Properties of Equality Whatever you do to one side of an equation

13. Properties of Equality do the same thing to the other side

14. Properties of Equality and the two sides will stay equal

15. Examples n – 6 = 9

16. Examples n – 6 = 9 Add 6 to both sides (addition property)

17. Examples n – 6 = 9 +6 +6

18. Examples n – 6 = 9 +6 +6 n = 3

19. Examples n = 3

20. Examples -35 = -5r

21. Examples -35 = -5r Divide both sides by -5 (division property)

22. Examples -35 = -5r -5 -5

23. Examples 7 = r

24. Examples -3(m + 3) = 16

25. Examples -3(m + 3) = 16 Distribute to get the m out of the parentheses

26. Examples -3(m + 3) = 16 -3m - 9 = 16 Distribute to get the m out of the parentheses

27. Examples -3(m + 3) = 16 -3m - 9 = 16 Add 9 to both sides (addition property)

28. Examples -3(m + 3) = 16 -3m - 9 = 16 +9 +9

29. Examples -3(m + 3) = 16 -3m - 9 = 16 +9 +9 -3m = 25

30. Examples -3(m + 3) = 16 -3m - 9 = 16 +9 +9 -3m = 25 Divide both sides by -3 (division property)

31. Examples -3m = 25 -3 -3

32. Examples m = -25 3

33. Examples 4s + 6s = 100

34. Examples 4s + 6s = 100 Combine like terms

35. Examples 4s + 6s = 100 10s = 100 Combine like terms

36. Examples 4s + 6s = 100 10s = 100 Divide each side by 10 (division property)

37. Examples 4s + 6s = 100 10s = 100 10 10

38. Examples s = 10

39. Examples 12 + 2g = 4 + 6g

40. Examples 12 + 2g = 4 + 6g Move the variable to one side of the equation

41. Examples 12 + 2g = 4 + 6g -2g -2g (subtraction property)

42. Examples 12 + 2g = 4 + 6g -2g -2g 12 = 4 + 4g

43. Examples 12 + 2g = 4 + 6g -2g -2g 12 = 4 + 4g Subtract 4 from both sides (subtraction property)

44. Examples 12 + 2g = 4 + 6g -2g -2g 12 = 4 + 4g -4 -4 8 = 4g

45. Examples 12 + 2g = 4 + 6g -2g -2g 12 = 4 + 4g -4 -4 8 = 4g Divide both sides by 4

46. Examples 12 + 2g = 4 + 6g -2g -2g 12 = 4 + 4g -4 -4 8 = 4g 4 4

47. Examples 2 = g

48. Today’s Work: Page 45 Problems 7-20 When you finish, you may work quietly on any homework you have.