1. Choose the biggest number in each pair of numbers below.
Starter
Choose the biggest number in each pair of numbers below.
7 and 1
-1 and 1
6 and 2
5 and -6
-2 and -1
0 and -4

2. What does equal mean?
Exactly the same value!
Complete the equations below by filling in the gaps – make sure both sides are equal.
5 + 6 = ___ ___ = 8 + 5
___ + 3 = = ___ + 6
___ + 11 = = 26 + ___ 3 6 9 6 12 19

3. Inequality Inequality Not equal to Greater than Less than
What is an inequality?
Inequality
Inequality
Not equal to
Greater than
Less than

4. For example, 6 is greater than 3
Inequality Symbols
>
greater than ≥
greater than or equal to
For example, 6 is greater than 3
6 > 3

5. Write five possible whole numbers which x can be for each inequality
3, 4, 5, 6, 7…
12, 13, 14, 15, 16…
-2, -1, 0, 1, 2…
18, 19, 20, 21, 22…

6. For example, 4 is less than 9
Inequality Symbols
<
less than ≤
less than or equal to
For example, 4 is less than 9
4 < 9

7. Starter – Inequalities Bingo
Draw a 3 x 3 grid and fill it with 9 of the inequalities from below.
x < -1
x < 0
x < 1
x < 2
x > -1
x > 0
x > 1
x > 2
x ≤ -1
x ≤ 0
x ≤ 1
x ≤ 2
x ≥ -1
x ≥ 0
x ≥ 1
x ≥ 2

24. Reminder on solving inequalities…
5x – 2 < 28
4x – 3 ≥ 2x + 7
+ 2
+ 2
- 2x
- 2x
5x < 30
2x – 3 ≥
÷ 5
÷ 5
+ 3
+ 3
x < 6
2x ≥
÷ 2
÷ 2
x ≥

25. Mrs. Bradshaw is making treats for a tea party later this week, and she has up to 15 eggs to use for this purpose. A batch of scones requires 2 eggs and a batch of miniature tarts requires 4 eggs. Write an inequality that describes this situation. 2s
+ 4t
≤ 15

26. Joe’s cell phone costs him $21 per month plus $3 for every 1GB of data downloaded. What is the limit to the number of GBs he can download to stay within his monthly budget of $30? 21
+ 3d
≤ 30
- 21
- 21
3d ≤ 7
÷ 3
÷ 3
d ≤ …
Joe can download 2 GB of data without going over his monthly budget.

27. 5h - 8 < h + 8 - h - h 4h - 8 < 8 + 8 + 8 4h < 16 ÷ 4 ÷ 4
Gloria starts with five times as much money as Hamish. Gloria gives £8 to Hamish, and then Hamish has more money than Gloria. How much money did Hamish start with?
5h - 8 < h + 8
- h
- h
4h - 8 <
+ 8
+ 8
4h <
÷ 4
÷ 4
h <
Hamish started with less than £4.

29. Answers
1. 4f + 10e ≥ 20
2. 7 books
3. 6 miles
4. 5 nights
5. 7 plants
6. 10 visits
7. Sam = 2, Alex = 5
Sam = 1, Alex = 4
Sam = 0, Alex = 3
8. 12 < x ≤ 13

30. Write five possible whole numbers which x can be for each inequality
9, 8, 7, 6, 5…
92, 91, 90, 89, 88…
-6, -7, -8, -9, -10…
6, 5, 4, 3, 2…
2, 1, 0, -1, -2…
0, -1, -2, -3, -4…

31. Which statements go with which inequality?
y is less than x
x < y
x is less than or equal to y
y is greater than or equal to x
x > y
x is less than y
y is less than or equal to x
x ≤ y
x is greater than or equal to y
y is greater than x
x ≥ y
x is greater than y

32. Put the correct symbols (< or >) between these pairs of numbers:
5 8
0 4
7 3
9 -2
2 -1
<
>
7 3
9 -2
2 -1
4 -6
-3 1
>
<
2 -1
4 -6
-3 1
-4 -9
-5 -1
>
<

33. Write five possible whole numbers which x can be for each inequality
6, 7, 8, 9
12, 13, 14, 15
-4, -3, -2, -1
3, 4, 5, 6, 7
12, 13, 14, 15, 16, 17, 18, 19
-2, -1, 0, 1, 2, 3

34. x ≥
x is greater than or equal to
x ≤
x is less than or equal to
x >
x is greater than
x <
x is less than

35. x ≥ 3
x < 10

36. x ≤ 5
2 < x ≤ 8

37. Pair Activity
Complete the Tarsia jigsaw, matching the inequalities to those displayed on the number lines.

39. Starter
3x + 8 = = 4x – 5
2x + 9 = = 4x + 5
12x – 25 = 5x – – 2x = 11 – 7x
7x – 42 = 2x – x – 5 = x + 15
2(5x + 2) = 4(2x + 3) 6(3x + 6) = 4(5x + 2)
5(2x + 3) = 3(3x + 5) 3(5x – 1) = 2(7x + 2)

40. Answers x = 1 x = 7 x = 5 x = -1 x = 3 x = 1 x = 7 x = -5 x = 4 x = 14

41. x ≥
x is greater than or equal to
x ≤
x is less than or equal to
x >
x is greater than
x <
x is less than

42. Solving Linear Inequalities
2x + 1 ≥ 7
-1 from both sides
2x ≥ 6
Divide both sides by 2
x ≥ 3

43. Solving Linear Inequalities
3(x – 4) < 18
Expand the brackets
3x – 12 < 18
+12 to both sides
3x < 30
Divide both sides by 3
x < 10

44. Solving Linear Inequalities
4(x – 4) ≤ x - 1
Expand the brackets
4x – 16 ≤ x - 1
-x from both sides
3x – 16 ≤ -1
+16 to both sides
3x ≤ 15
x ≤ 5
Divide both sides by 3

46. Answers

47. Graphing Inequalities
SOLID line if less/greater than or equal to
On a set of axes, show the set of values that satisfy the inequality; x ≤ 2 Draw the line showing; x = 2 But the inequality is saying a range of values…

48. Graphing Inequalities
DOTTED line if less/greater than but not equal to
On a set of axes, show the set of values that satisfy the inequality; y < -5 Draw the line showing; y = -5 But the inequality is saying a range of values…

49. Graphing Inequalities
On a set of axes, show the set of values that satisfy the inequality; y > x Draw the line showing; y = x But the inequality is saying a range of values…

51. A
x < 5 B
x ≤ 5 C
y < 5 D
y ≤ 5

52. A
x > 5 B
x ≥ 5 C
y > 5 D
y ≥ 5

53. A B C D

54. A B C D

55. A B C D

56. A B C D