1. Sir E Scott School Mathematics
Presents
Equations

2. x + 5 = 20

3. x + 5 = 20
x+5 20
(-5)

4. x + 5 = 20 x 20
(-5)

5. x + 5 = 20 x 15
x = 15

6. x + 5 = 20
Example 1:
x + 5 = 20
(-5) (-5)
x = 15

7. 1) x + 8 = 12 2) a + 12 = 30 (-8) (-8) (-12) (-12) x = 4 a = 18
Answers
Exercise A
1) x + 8 = 12 2) a + 12 = 30
(-8) (-8)
x = 4
(-12) (-12)
a = 18
3) 5 + x = 13 4) b + 7 = 42
(-5) (-5)
x = 8
(-7) (-7)
b = 35

8. 3x + 7 = 25

9. 3x + 7 = 25
3x+7 25
(-7)

10. 3x + 7 = 25 3x 25
(-7)

11. 3x + 7 = 25 3x 18 ?
3x = 18

12. 3x = 18 x = 6 This means 3 times x equals 18 3 times 6 equals 18
So x must be 6
x = 6

13. 3x + 7 = 25
Example 2:
3x + 7 = 25
(-7) (-7)
3x = 18
x = 6

14. 1) 2x + 7 = 23 2) 6a + 11 = 29 (-7) (-7) 2x = 16 x = 8 (-11) (-11)
Answers
Exercise B
1) 2x + 7 = ) 6a + 11 = 29
(-7) (-7)
2x = 16
x = 8
(-11) (-11)
6a = 18
a = 3
3) 5 +8y = ) 9 + 3d = 42
(-5) (-5)
8y = 32
y = 4
(-9) (-9)
3d = 33
d = 11

15. 5x - 6 = 44

16. 5x - 6 = 44
5x-6 44
(+6)

17. 5x - 6 = 44 44
(+6) 5x

18. 5x - 6 = 44 5x 50
5x = 50

19. 5x - 6 = 44
Example 3:
5x - 6 = 44
(+6) (+6)
5x = 50
x = 10

20. 1) 5b - 8 = 12 2) 7a - 9 = 33 (+9) (+9) (+8) (+8) 7a = 42 5b = 20
Answers
Exercise C
1) 5b - 8 = 12 2) 7a - 9 = 33
(+9) (+9)
7a = 42
a = 6
(+8) (+8)
5b = 20
b = 4
3) 6y - 6 = 30 4) 9z- 7 = 20
(+7) (+7)
9z = 27
z = 3
(+6) (+6)
6y = 36
y = 6

21. Is there a
shortcut?

22. Change side, change sign
5x - 6 = 44
- 6

23. Change side, change sign
5x = 44
+ 6
5x = 50
x = 10

24. 5x - 6 = 44
Example 4:
5x - 6 = 44
5x =
5x = 50
x = 10

25. Change side, change sign
3x + 7 = 25

26. Change side, change sign
3x = 25
- 7
3x = 18
x = 6

27. 3x + 7 = 25
Example 5:
3x + 7 = 25
3x =
3x = 18
x = 6

28. Answers
Exercise D
1) 2a + 7 = 23
2a =
2a = 16
a = 8
2) 7x - 9 = 33
7x =
7x = 42
x = 6

29. Tricky one!
6x = 9 + 2x
+ 2x
6x – 2x = 9 ?
4x = 9

30. The 4 is multiplying the x, so when it changes side, it divides.
Change side, change sign 4
4x = 9
The 4 is multiplying the x, so when it changes side, it divides.

31. Change side, change sign4
4x = 9
x = 9 ÷ 4
x = 2.25

32. 5x + 2 = 3x + 6

33. 5x + 2 = 3x + 6
5x+2
3x+6
(-2)

34. 5x + 2 = 3x + 6 5x
3x+6
(-2)

35. 5x + 2 = 3x + 6 5x
3x+4
(-3x)

36. 5x + 2 = 3x + 6 4 5x
(-3x)

37. 5x + 2 = 3x + 6 2x 4
2x = 4
So x = 2

38. Change side, change sign
5x + 2 = 3x + 6
+ 2
5x = 3x
5x = 3x + 4 3x
5x –3x = 4
2x = 4
x = 2

39. Change side, change sign
Most Xs are on the right.
So this time:
Xs on the right,
numbers on the left! 3x 8x
3x + 6 = 8x - 4
- 4
3x = 8x
3x + 10 = 8x 3x
10 = 8x – 3x
10 = 5x
x = 2

40. 3x + 6 = 8x - 4 Example 6: 3x + 6 = 8x - 4 6+4 = 8x – 3x 10 = 5x x = 2
Try two changes
together!
6+4 = 8x – 3x
10 = 5x
x = 2

41. 1) 5a + 7 = 2a + 22 5a – 2a = 22 - 7 3a = 15 a = 5 2) 3x + 9 = 7x - 15
Answers
Exercise E
1) 5a + 7 = 2a + 22
5a – 2a =
3a = 15
a = 5
2) 3x + 9 = 7x - 15
= 7x – 3x
24 = 4x
x = 6

42. Sir E Scott School Mathematics
Presents
Inequations

43. Inequations 8 9 9 8
is greater
than
>

44. Inequations 5 9 5
< 9
is less
than

45. Hint: The less than sign is almost L shaped.
Remember
is greater than
is less than
Hint: The less than sign is almost L shaped.
<
<
<
ess than

46. Click here for number line
Practice: fill in the correct sign
(2)
(4)
(6)
(7) (8)
(9) (10)
<
>
<
>
>
<
<
<
>
<
Click here for number line

47. To drive, what age do you have to be?
To get married in Scotland, what age do you have to be?
To buy alcohol, what age do you have to be?
Click on the picture to reveal the answer.

48. What speed should you drive at in town?
How many passengers can a black taxi take?
Click on the picture to reveal the answer.

49. is greater than or equal to
Quick Check!
is greater than or equal to
Next question A B C D

50. Quick Check!
is less than
Next question A B C D

51. Quick Check!
is greater than
Next question A B C D

52. Quick Check!
is less than or equal to
Finish A B C D

53. Use the same method as for equations!
Solving inequations
Use the same method as for equations!
3a + 8 < 26
+ 8
- 8
3a < 18
a < 6

54. 3a + 8 < 26 a < 6 Example: 3a + 8 < 26 3a < 26 - 8

55. (HSDU Support Materials))
Now do Exercise ?
(HSDU Support Materials))

56. greater than or equal to
Aged
greater than or equal to 18

57. greater than or equal to
Aged
greater than or equal to 17

58. greater than or equal to
Aged
greater than or equal to 16

59. Speed
less than or equal to
30 mph

60. Passengers
less than or equal to 5

61. Negative Positive Number Line negative numbers positive numbers -1 -2-3 -4 -5 -6 -7 1 2 3 4 5 6 7
negative numbers
Negative Positive
positive numbers

62. Try again!

63. Correct!