1. 20/11/2018
INEQUALITY NOTATION

2. 20/11/2018 Symbols …is EQUAL to …is APPROXIMATELY equal to
…is NOT equal to
…is LESS THAN
…is GREATER THAN
…is less than OR EQUAL TO
…is greater than OR EQUAL TO

3. 20/11/2018
Task – read the following inequalities and write what they mean in words
1. x > 9
x is greater than 9
2. x > -1
x is greater than -1
3. p  6
p is greater than or equal to 6
4. a  - 4
a is greater than or equal to - 4
< n < 3
n is greater than 0 but less than 3
 n < 2
n is greater than or equal to -5 but less than 2
 n  -1
n is greater than or equal to -7 but less than or equal to -1

4. 20/11/2018
Number line notation
A HOLLOW circle means that the number itself is NOT included
So means < or >
A SOLID circle means that the number itself IS included
So means ≤ or ≥

5. 20/11/2018 Examples x < 9 ‘x is less than 9 x > 5
‘x is greater than 5’ 5
x ≤ 6
‘x is less than or equal to 5’ 6
3 ≤ x < 10
‘x is greater than or equal to 3 but less than 10’ 3 10

6. 20/11/2018 x  -2 x > 4 x  -2 x < 4 -5  n  5 -1 < n  4
Task – Write down the inequality represented by each number line
x  -2 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6
x > 4 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6
x  -2 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6
x < 4 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6
-5  n  5 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6
-1 < n  4 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6
-5 < n < 0 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6
-3  n < 6 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6

7. 20/11/2018
Task – draw a number line to represent each of these inequalities
0  n  5 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6
-5 < n  4 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6
0 < n < 5 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6
-5  n < -3 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6

8. FINDING INTEGER SOLUTIONS
20/11/2018
FINDING INTEGER SOLUTIONS

9. List the integer values that satisfy this inequality.
20/11/2018
Integer values that satisfy an inequality
Integer means WHOLE NUMBER
Just write down all the whole numbers that make the inequality true
Example
–3 < x ≤ 5
List the integer values that satisfy this inequality.
The integer values that satisfy this inequality are
–2, –1, 0, 1, 2, 3, 4, 5.

10. 20/11/2018
Discussion – how many inequalities can you find which describe this list of integers
–4, –3, –2, –1, 0, 1
There are four possible inequalities that give this solution set,
–5 < x < 2
–4 ≤ x < 2
–5 < x ≤ 1
–4 ≤ x ≤ 1

11. 20/11/2018
Exam questions

12. On your mini whiteboards… Quick Questions!
20/11/2018
INTEGER SOLUTIONS
On your mini whiteboards… Quick Questions!

13. 20/11/2018
n ≤ 6
. . .1,2,3,4,5
7,8,9,10 …
6,5,4,3…
6 ,7 ,8,9…

14. 20/11/2018
p ≥ 8
9,10,11,…
….2,3,4,5,6,7
…5,6,7,8
8, 9,10,11…

15. 20/11/2018
n < 4
4,5,6,7…
3,4,5,6…
3,2,1…..
4,3,2,1….

16. 20/11/2018
w > -1
0,1,2,3,4…
-1, 0, 1, 2…
-1,-2,-3,-4 …
-2,-3,-4,…

17. 20/11/2018
p ≤ -5
-4,-3,-2….
-5 -6,-7,-8…
5,6,7,8..
-5,-4,-3…

18. 20/11/2018
2 ≤ n < 6
1,2,3,4,5,6
2,3,4,5,6
2,3,4,5
3,4,5,6

19. 20/11/2018
-3 ≤ n < 5
-2,-1, ,4,5
-4,-3,-2…3,4,5
-3 -2,-1 …4,5
-3,-2,-1 … 3,4

20. 20/11/2018
n ≤ 6
5,4,3,2,1…
6,7,8,9,….
6,5,4,3 ….
7, 8,9,10 …

21. 20/11/2018
n +1 < 6
5,4,3,2….
6,7,8,9 ….
4,3,2,1….
5,6,7,8 …

22. 20/11/2018
5p ≥ 30
5,6,7,8 ….
6,5,4,3,2,1 ….
7,8,9,10 ….
6,7,8,9 ….

23. 20/11/2018
n – 3 > 7
10,11,12,13….
10,9,8,7,6…..
11,12,13,14….
9,8,7,6,5 ….

24. 20/11/2018
SOLVING INEQUALITIES

25. 20/11/2018
Solving inequalities
Solve exactly as if it were an equation
The only difference is if you want to × or ÷ by a NEGATIVE
You must FLIP THE INEQUALITY

26. 20/11/2018
Example
Solve 2𝑥 − 1 ≤ 4

27. 20/11/2018
Example
Solve 2𝑥 + 3 ≤ 5𝑥 + 7

28. 20/11/2018
Example
Solve – 3𝑥 < 𝑥

29. Mini whiteboards… Quick Questions!
20/11/2018
SOLVING INEQUALITIES
Mini whiteboards… Quick Questions!

30. 20/11/2018
Solve
3t - 4 > 11
t > 5

31. 20/11/2018
Solve
3y - 12 ≤ y - 4
y ≤ 4

32. 20/11/2018
Solve
7 < 2x + 1 < 13
3 < x < 6

33. 20/11/2018
Solve
11 ≤ 3x + 5 < 17
2 ≤ x < 4

34. 20/11/2018
Solve
7 - 2x > 5x - 7
x < 2

35. 20/11/2018
Solve
-3x < -x + 8
x > -4

36. Solve the inequality 3𝑥 – 5 > 13
20/11/2018
Solve the inequality 3𝑥 – 5 > 13
𝑥 > 6
Solve the inequality 2𝑥 – 3 < 6
𝑥 < 4.5

37. Solve the inequality 5𝑥 – 3 > 3𝑥 + 5
20/11/2018
Solve the inequality 5𝑥 – 3 > 3𝑥 + 5
𝑥 > 4
Solve the inequality 𝑥 – 7 < 4𝑥 + 2
𝑥 <−3

38. 20/11/2018
Harder types

39. 20/11/2018
Example
Solve 12<10+ 3𝑥<52

40. Solve the inequality 5 < 2𝑥 – 1 < 13
20/11/2018
Solve the inequality 5 < 2𝑥 – 1 < 13
3 < 𝑥 < 7
Solve the inequality 2 < 12 – 5𝑥 < 27
2 > 𝑥 > −3 OR
−3 < 𝑥 < 2