1. Solving Linear Equations

2. And the Secret IS…
When Solving Linear equations you must do the opposite
That is what algebra is all about,,,
…it’s doing the opposite.

3. Add = __________ Subtract = __________ Multiply = __________
Now another set.
Add = __________
Subtract = __________
Multiply = __________
Divide = __________

4. Subtract Add = __________ Add Subtract = __________ Divide
Your answers should have been…
Subtract
Add = __________
Add
Subtract = __________
Divide
Multiply = __________
Divide = __________
Multiply

5. + = __________ - = __________ ( )( ) = __________ / = __________
One last set.
+ = __________
- = __________
( )( ) = __________
/ = __________

6. - ÷ x + = __________ + - = __________ ( )( ) = __________
Your answers should have been… -
+ = __________ +
- = __________ ÷
( )( ) = __________ x
/ = __________

7. One Step Equations
Now you are going to work on solving some Algebra problems Remember…
ITS ALL ABOUT DOING
OPPOSITE!!!

8. One Step Equations
X + 3 = 17
What Side of the equation you are going to work with ?
The Rights side
The lefts side

9. One Step Equations
X + 3 = 17
What Side of the equation you are going to work with ?
The lefts side
…Because that’s where the varible is.

10. One Step Equations
X + 3 = 17
Click on the answer below that is the opposite .
Add 3
Subtract 3
Multiply 3
Divide 3

11. One Step Equations
Good Job!
The correct answer is subtract 3.

12. One Step Equations
4x = 20
What Side of the equation you are going to work with ?
The Rights side
The lefts side

13. One Step Equations
4x = 20
What Side of the equation you are going to work with ?
The lefts side
…Because that’s where the variable is.

14. One Step Equations
4x = 20
Click on the answer below that is the opposite.
Add 4
Subtract 4
Multiply by 4
Divide by 4

15. One Step Equations
x 5
10 =
What Side of the equation you are going to work with ?
The Rights side
The lefts side

16. One Step Equations
x 5
10 =
What Side of the equation you are going to work with ?
The Rights side
…Because that’s where the variable is.

17. One Step Equations
x 5
10 =
Click on the answer below that is the opposite .
Add 5
Subtract 5
Multiply by 5
Divide by 5

18. One Step Equations
Good!
The correct answer is multiply by 5.

19. One Step Equations
8 = X – 7
What Side of the equation you are going to work with ?
The Rights side
The lefts side

20. One Step Equations
8 = X – 7
What Side of the equation you are going to work with ?
The Rights side
…Because that’s where the variable is.

21. One Step Equations
8 = X – 7
Click on the answer below that is the opposite of.
+ 7
- 7
x 7
÷ 7

22. One Step Equations
Congratulations!

23. One Step Equations Opposite!
Alright, now you are going to actually solve some problems. This is nothing to be worried about, just remember one word…
Opposite!

24. One Step Equations
X + 5 = 13
What Side of the equation you are going to work with ?
The Rights side
The lefts side

25. One Step Equations
X + 5 = 13
What Side of the equation you are going to work with ?
The lefts side
…Because that’s where the variable is.

26. One Step Equations
X + 5 = 13
Click on the answer below that is the opposite.
+ 5
- 5
x 5
÷ 5

27. X + 5 = 13 -5 -5 _________ One Step Equations
You subtract – 5 in both side of the equatiion .

28. X + 5 = 13 - 5 - 5 _________ X = 8 One Step Equations X = 8
You drop down the X and equal sign.
Cancel 5
Drop down “=“ sign.
And then subtract 13 – 5 = 8.

29. One Step Equations
15 =X - 9
What Side of the equation you are going to work with ?
The Rights side
The lefts side

30. One Step Equations
15 =X - 9
What Side of the equation you are going to work with ?
The Rights side
…Because that’s where the variable is.

31. One Step Equations
15 =X - 9
Click on the answer below that is the opposite.
+ 9
- 9
x 9
÷ 9

32. 15 = X - 9 + 9 +9 _________ X 24 = One Step Equations
You add + 9 in both side of the equation .
Now add gives you 24.
You drop down “ =“ sign then X
Cancel 9

33. One Step Equations
2x = 18
What Side of the equation you are going to work with ?
The Rights side
The lefts side

34. One Step Equations
2x = 18
What Side of the equation you are going to work with ?
The lefts side
…Because that’s where the variable is.

35. One Step Equations
2x = 18
Click on the answer below that is the opposite.
+ 2
- 2
x 2
÷ 2

36. ___ 2x = 18 __ _________ 2 2 1 x 9 = One Step Equations ÷
You divide by 2 in both side.
Now 2 divide 2 gives you 1 x.
You drop down “ =“
Now add gives you 9. ÷

37. ___ 2x = 18 __ _________ 2 2 1 x 9 = One Step Equations
Do we really have to write the 1 in
Front of the X.
No.

38. One Step Equations
24 = 4x
What Side of the equation you are going to work with ?
The Rights side
The lefts side

39. One Step Equations
24 = 4x
What Side of the equation you are going to work with ?
The Rights side
…Because that’s where the variable is.

40. ___ __ 24 = 4x _________ 6 = x 1 One Step Equations 4 4
___ __
24 = 4x
_________ 4 4 6 = x 1
You divide by 4 in both side.
Now 24 divide 4 gives you 6.
You drop down “ =“
Now 4 divide 4 gives you 1 x.

41. ___ __ 24 = 4x _________ 6 = x 1 One Step Equations 4 4
___ __
24 = 4x 4
_________ 4 6 = x 1
Do we really have to write the 1 in
Front of the X.
No.

42. One Step Equations
x 3
= 12
What Side of the equation you are going to work with ?
The Rights side
The lefts side

43. One Step Equations
x 3
= 12
What Side of the equation you are going to work with ?
The lefts side
…Because that’s where the variable is.

44. One Step Equations
x 3
= 12
Click on the answer below that is the opposite.
+ 3
- 3
x 3
÷ 3

45. x 3 3• = 12 •3 ___________ 1 x = 36 One Step Equations
You multiply by 3 in both side.
Now 3 divide 3 gives you 1X.
You drop down “ =“
Now 12 multiply by 3 equals 36.

46. x 3 3• = 12 •3 ___________ 1 x = 36 One Step Equations
Do we really have to write the 1 in
Front of the X.
No.

47. 5X - 3 = 12 Two Steps Equations
What Side of the equation you are going to work with ?
The Rights side
The lefts side

48. 5X - 3 = 12 Two Steps Equations
What Side of the equation you are going to work with ?
The lefts side
…Because that’s where the variable is.

49. 5X - 3 = 12 Two Steps Equations
What the first step you are going to do?
add then divide by 5
divide 5 then add by 3

50. 5X - 3 = 12 Two Steps Equations
What the first step you are going to do?
add then divide by 5

51. 5X - 3 = 12 +3 +3 ___________ = 5X 15 Two Steps Equations
You add by 3 in both side.
You drop down 5x
Cancel 3
You drop down =
Now 12 plus 3 gives you 15.

52. 5X - 3 = 12 ___________ +3 +3 = 5X __ 15 __ ___________ 5 5 1 x = 3
Two Steps Equations
5X - 3 = 12
___________ +3 +3 = 5X __ 15 __
___________ 5 5 1 x = 3
Now divide by 5 in both sides
Now 5 divide 5 gives you 1X.
You drop down “ =“
Now 15 divide by 5 equals 3

53. 5X - 3 = 12 +3 +3 ___________ = 5X __ 15 __ ___________ 5 5 1 x = 3
Two Steps Equations
5X - 3 = 12 +3 +3
___________ = 5X __ 15 __
___________ 5 5 1 x = 3
Do we really have to write the 1 in
Front of the X.
No.

54. - 44= - 8 - 6X Two Steps Equations
What Side of the equation you are going to work with ?
The Rights side
The lefts side

55. - 44= - 8 - 6X Two Steps Equations
What Side of the equation you are going to work with ?
The Rights side
…Because that’s where the variable is.

56. - 44= - 8 - 6X Two Steps Equations
What the first step you are going to do?
add then divide by -6
divide then add by

57. - 44= - 8 - 6X Two Steps Equations
What the first step you are going to do?
add then divide by -6

58. - 44 = - 8 - 6X +8 +8 ___________ - 6X -36 = Two Steps Equations
You add + 8 in both side.
Now -44 plus 8 gives you -36.
You drop down “ =“
Cancel 8
Now You drop down -6x

59. - 44 = - 8 - 6X ___________ +8 +8 - 6X -36 __ = __ ___________ -6 -6 6
Two Steps Equations
- 44 = X
___________ +8 +8
- 6X
-36 __ = __
___________ -6 -6 6 = X
Now divide by -6 in both sides
Now -36 divide -6 gives you 6.
Now -6 divide -6 gives you 1X.

60. 3
( 5 X – 3 ) = 21 _ ( 21 15 X ) = 9
The Distributive Property says that the number in front of the parentheses can be multiplied by each term in side the parentheses.
Now 3 multiply by 5 equals 15
Add 3 multiply by 3 equals 9

61. 3
( 5 X – 3 ) = 21 _ ( ) 21 15 X = 9
Do you need the parenthesis ? No

62. 3 ( 5 X – 3 ) = 21 _ 15 X = 21 9 _____________ + 9 + 9 = 15 X 30 =
Add 9 in both sides
You drop 15 X
Cancel 9
Drop = sign
Add = 30

63. 3 ( 5 X – 3 ) = 21 _ 15 X = 21 9 _____________ + 9 + 9 = 15 X _ 30 _
Divide 15 in both sides
15 divide by 15 equals 1 x

64. 3 ( 5 X – 3 ) = 21 _ = 21 15 X 9 _____________ + 9 + 9 = 1 X 30 _ 15 =
Divide 15 in both sides
15 divide by 15 equals 1 x

65. 3 ( 5 X – 3 ) = 21 _ 15 X = 21 9 _____________ + 9 + 9 = 1 X 30 _ 15 =
Divide 15 in both sides
15 divide by 15 equals 1 x
30 divide 15 = 2

66. 3 ( 5 X – 3 ) = 21 _ 15 X = 21 9 _____________ + 9 + 9 = 1 X 30 _ 15 =
Divide 15 in both sides
15 divide by 15 equals 1 x
30 divide 15 = 2

67. 3 ( 5 X – 3 ) = 21 _ = 21 15 X 9 _____________ + 9 + 9 = 1 X 2 =
Divide 15 in both sides
15 divide by 15 equals 1 x
30 divide 15 = 2

68. 3 ( 5 X – 3 ) = 21 _ = 21 15 X 9 _____________ + 9 + 9 = 1 X 2 =
Divide 15 in both sides
15 divide by 15 equals 1 x
30 divide 15 = 2

69. 10X - 15 = 5X+10 -5X ______________ -5X Variables in Both Sides
You subtract – 5x in both side.

70. 10X - 15 = 5X+10 -5X ______________ -5X - 5X 15 = 10
Variables in Both Sides
10X - 15 = 5X+10
______________
-5X
-5X - 5X 15 = 10
Subtract 10X - 5X = 5X
Drop - sign
Drop 15 %X
Drop = sign
Cancel 5X
Drop 10

71. 10X - 15 = 5X+10 -5X ______________ -5X - 5X 15 = 10 +15 +15
Variables in Both Sides
10X - 15 = 5X+10
______________
-5X
-5X - 5X 15 = 10
+15
+15
______________
Add + 15 in both side.

72. 10X - 15 = 5X+10 -5X ______________ -5X - 5X 15 = 10 +15 +15
Variables in Both Sides
10X - 15 = 5X+10
______________
-5X
-5X - 5X 15 = 10
+15
+15
______________ 25 5X =
Drop the 5X
Cancel 15 and Drop the = sign
Add = 25

73. 10X - 15 = 5X+10 ______________ -5X -5X - 5X 15 = 10 +15 +15
Variables in Both Sides
10X - 15 = 5X+10
______________
-5X
-5X - 5X 15 = 10
+15
+15
______________ 25 5X = __ __ 5 5
Divide by 5 in both side.

74. 10X - 15 = 5X+10 ______________ -5X -5X - 5X 15 = 10 +15 +15
Variables in Both Sides
10X - 15 = 5X+10
______________
-5X
-5X - 5X 15 = 10
+15
+15
______________ 25 5X = __ __ 5 5 1 X = 5

75. 10X - 15 = 5X+10 ______________ -5X -5X - 5X 15 = 10 +15 +15
Variables in Both Sides
10X - 15 = 5X+10
______________
-5X
-5X - 5X 15 = 10
+15
+15
______________ 25 5X = __ __ 5 5 1 X = 5

76. Congratulations
We Finished