2. Simplify 1)
27 + (-86) 3)
-43 - (-28) 2) 4)

3. One-Step Equations
By:
Jennifer Cassidy

4. Solving Equations is like detective work.
Use your clues
Work backwards

5. Undoing an equation is similiar to a detective retracing steps
Follow the criminals steps in reverse
This will lead you to the culprit ( the value of the variables)

6. How much does
X weigh ? X

7. What can we do to get x
by himself ? X

8. We can subtract 25 pounds
from the left side X

9. X

10. We must subtract 25 from the other side to keep it balancedX

11. So how much does x weigh? X

12. x = 15

13. In other words
x + 25 = 40
x = 15
x = 15

14. Let’s Check
x + 25 = 40
x = 15
= 40
40 = 40
So, x = 15 is the correct answer

15. Let’s try another
x + 50 = 146
x = 9 6
x = 9 6

16. Let’s check
x + 50 = 146
x = 96
= 146
146 = 146
So, x = 96 is the right answer

17. I have a problem. A friend of mine lost 5 pounds
I have a problem. A friend of mine lost 5 pounds. The next week she went on a cruise and gained the 5 pounds back. Overall, did she loose any weight?
Why?

18. This is called a zero pair. They cancel each other out
This is called a zero pair. They cancel each other out. In other words, they do not weigh anything.
-1 and +1
- +

19. -4 and +4
- +
- +

20. Let’s say we have 7 positives, what can we add to 7 to get zero?
7 negatives

21. + -

22. + -

23. Now, let’s try a different type of problem.X

24. What will the x need to do to the 10 negatives so that he can be by himself?
He will need to get rid of them.

25. How do we get rid of them?
To get rid of the negatives, we will need to combine them with something to get zero.

26. What can we combine them with to get zero?
10 positives.

27. Now let’s add 10 positives to the left side.X

28. OH NO !!!!!!! X

29. We need to add 10 positives
to the other side ! ! X

30. Whew! X

31. Now, don’t these
combine to make zero? X

32. So, let’s take them away. X

33. So what does X equal ? X

34. x = 30

35. In other words, this is all we did.
x + (-10) = 20
x = 30
x = 30

36. Let’s check x + (-10) = 20 x = 30 30 + (-10) = 20 20 = 20
So, x = 30 is the right answer

37. -5 + X = 16 X

38. What can we add to 5 negatives to get zero?X

39. 5 positives!!! X

40. Oh No!!! We need to do the same on the other side!!X

41. Whew!!! X

42. Now, don’t these combine to make zero?X

43. Well, let’s take them away!X

44. So, what does x equal? X

45. x = 21

46. In other words,
- 5 + x = 16
0 + x = 21
x = 21

47. Let’s check -5 + x = 16 x = 21 -5 + 21 = 16 16 = 16
= 16
16 = 16
So, x = 21 is correct!!!

48. Let’s try one more. t + (-10) = -18

49. Add 10 positives to one side.

50. Then add 10 positives to the other side.

51. Take away your zero pairs

52. When we take away our zero pairs what do we have left?

53. t = -8 t

54. In other words
t + (-10) = -18
t = -8
t = -8

55. Let’s check t + (-10) = -18 t =-8 -8 + (-10) = -18 -18 = -18
-8 + (-10) = -18
-18 = -18
So, t = -8 is the right answer

56. Let’s try some more!

57. y + 21 = -7

58. y + 21 = - 7
y = -28
y = -28

59. What if we had something a little different.

60. We need to change it to an addition statement.
From: y - 12 = 42
To: y + (-12) = 42
Remember to add the opposite!!!

61. Now we can solve it.
y + (-12) = 42
= 12
y + 0 = 54
y = 54

62. Now try, -17 = y - ( -9 )

63. -17 = y - ( -9)
-17 = y + 9
-26 = y + 0
-26 = y