The document discusses how to solve equations by making the variable the subject of the formula. It provides examples of solving equations such as x + 3 = 6, 5z = 45, and 4(a - 5) = 16 for the variable. The document also discusses when the inequality sign changes, such as when multiplying or dividing by a negative number, or taking the reciprocal of both sides. Examples are provided of solving inequalities like 6x < 36 and -4 ≤ -4x ≤ 8 for the variable.

1. Equations/Inequations

2. Equations/Inequations
Make the pronumeral the subject of the formula

3. Equations/Inequations
Make the pronumeral the subject of the formula
e.g. (i ) x  3  6

4. Equations/Inequations
Make the pronumeral the subject of the formula
e.g. (i ) x  3  6

5. Equations/Inequations
Make the pronumeral the subject of the formula
e.g. (i ) x  3  6
x  63
x3

6. Equations/Inequations
Make the pronumeral the subject of the formula
e.g. (i ) x  3  6
x  63
x3
(ii ) 5 z  45

7. Equations/Inequations
Make the pronumeral the subject of the formula
e.g. (i ) x  3  6
x  63
x3
(ii ) 5 z  45
45
z
5
z 9

8. Equations/Inequations
Make the pronumeral the subject of the formula
e.g. (i ) x  3  6
x  63
x3
(ii ) 5 z  45
45
z
5
z 9
(iii ) 4  a  5   16

9. Equations/Inequations
Make the pronumeral the subject of the formula
e.g. (i ) x  3  6
x  63
x3
(ii ) 5 z  45
45
z
5
z 9
(iii ) 4  a  5   16
4a  20  16
4a  36
a9

10. Equations/Inequations
Make the pronumeral the subject of the formula
e.g. (i ) x  3  6 (iv) 3z  2  z  9
x  63
x3
(ii ) 5 z  45
45
z
5
z 9
(iii ) 4  a  5   16
4a  20  16
4a  36
a9

11. Equations/Inequations
Make the pronumeral the subject of the formula
e.g. (i ) x  3  6 (iv) 3z  2  z  9
x  63
x3
(ii ) 5 z  45
45
z
5
z 9
(iii ) 4  a  5   16
4a  20  16
4a  36
a9

12. Equations/Inequations
Make the pronumeral the subject of the formula
e.g. (i ) x  3  6 (iv) 3z  2  z  9
x  63 2 z  11
x3 11
z
(ii ) 5 z  45 2
45
z
5
z 9
(iii ) 4  a  5   16
4a  20  16
4a  36
a9

13. Equations/Inequations
Make the pronumeral the subject of the formula
e.g. (i ) x  3  6 (iv) 3z  2  z  9
x  63 2 z  11
x3 11
z
(ii ) 5 z  45 2
45
z 5 2
5 (v )  3
z 9 7y y
(iii ) 4  a  5   16
4a  20  16
4a  36
a9

14. Equations/Inequations
Make the pronumeral the subject of the formula
e.g. (i ) x  3  6 (iv) 3z  2  z  9
x  63 2 z  11
x3 11
z
(ii ) 5 z  45 2
45
z 5 2
5 (v )  3
z 9 7y y
5  14  21y
(iii ) 4  a  5   16
4a  20  16
4a  36
a9

15. Equations/Inequations
Make the pronumeral the subject of the formula
e.g. (i ) x  3  6 (iv) 3z  2  z  9
x  63 2 z  11
x3 11
z
(ii ) 5 z  45 2
45
z 5 2
5 (v )  3
z 9 7y y
5  14  21y
(iii ) 4  a  5   16 21 y  19
4a  20  16 19
4a  36 y
21
a9

16. Equations/Inequations
Make the pronumeral the subject of the formula
e.g. (i ) x  3  6 (iv) 3z  2  z  9 x  3 2x  6
(vi ) 
x  63 5 3
2 z  11
x3 11
z
(ii ) 5 z  45 2
45
z 5 2
5 (v )  3
z 9 7y y
5  14  21y
(iii ) 4  a  5   16 21 y  19
4a  20  16 19
4a  36 y
21
a9

17. Equations/Inequations
Make the pronumeral the subject of the formula
e.g. (i ) x  3  6 (iv) 3z  2  z  9 x  3 2x  6
(vi ) 
x  63 5 3
2 z  11
x3 11
z
(ii ) 5 z  45 2
45
z 5 2
5 (v )  3
z 9 7y y
5  14  21y
(iii ) 4  a  5   16 21 y  19
4a  20  16 19
4a  36 y
21
a9

18. Equations/Inequations
Make the pronumeral the subject of the formula
e.g. (i ) x  3  6 (iv) 3z  2  z  9 x  3 2x  6
(vi ) 
x  63 5 3
2 z  11 3 x  9  10 x  30
x3 11
z
(ii ) 5 z  45 2
45
z 5 2
5 (v )  3
z 9 7y y
5  14  21y
(iii ) 4  a  5   16 21 y  19
4a  20  16 19
4a  36 y
21
a9

19. Equations/Inequations
Make the pronumeral the subject of the formula
e.g. (i ) x  3  6 (iv) 3z  2  z  9 x  3 2x  6
(vi ) 
x  63 5 3
2 z  11 3 x  9  10 x  30
x3 11
z 7 x  39
(ii ) 5 z  45 2
39
45 x
z 5 2 7
5 (v )  3
z 9 7y y
5  14  21y
(iii ) 4  a  5   16 21 y  19
4a  20  16 19
4a  36 y
21
a9

20. The inequality sign will only change when:

21. The inequality sign will only change when:
1) Multiply or divide by a negative number
“if you change the sign, you change the sign”

22. The inequality sign will only change when:
1) Multiply or divide by a negative number
“if you change the sign, you change the sign”
2) The reciprocal of both sides are taken

23. The inequality sign will only change when:
1) Multiply or divide by a negative number
“if you change the sign, you change the sign”
2) The reciprocal of both sides are taken
e.g. (i ) 6 x  36

24. The inequality sign will only change when:
1) Multiply or divide by a negative number
“if you change the sign, you change the sign”
2) The reciprocal of both sides are taken
e.g. (i ) 6 x  36
x6

25. The inequality sign will only change when:
1) Multiply or divide by a negative number
“if you change the sign, you change the sign”
2) The reciprocal of both sides are taken
e.g. (i ) 6 x  36
x6
5 6 7

26. The inequality sign will only change when:
1) Multiply or divide by a negative number
“if you change the sign, you change the sign”
2) The reciprocal of both sides are taken
e.g. (i ) 6 x  36 (ii ) 2  6  4 x  14
x6
5 6 7

27. The inequality sign will only change when:
1) Multiply or divide by a negative number
“if you change the sign, you change the sign”
2) The reciprocal of both sides are taken
e.g. (i ) 6 x  36 (ii ) 2  6  4 x  14
x6 4  4 x  8
5 6 7

28. The inequality sign will only change when:
1) Multiply or divide by a negative number
“if you change the sign, you change the sign”
2) The reciprocal of both sides are taken
e.g. (i ) 6 x  36 (ii ) 2  6  4 x  14
x6 4  4 x  8
1  x  2
5 6 7

29. The inequality sign will only change when:
1) Multiply or divide by a negative number
“if you change the sign, you change the sign”
2) The reciprocal of both sides are taken
e.g. (i ) 6 x  36 (ii ) 2  6  4 x  14
x6 4  4 x  8
1  x  2
5 6 7 2  x  1

30. The inequality sign will only change when:
1) Multiply or divide by a negative number
“if you change the sign, you change the sign”
2) The reciprocal of both sides are taken
e.g. (i ) 6 x  36 (ii ) 2  6  4 x  14
x6 4  4 x  8
1  x  2
5 6 7 2  x  1
-2 1

31. The “correct” way of writing inequalities

32. The “correct” way of writing inequalities
4 5 6

33. The “correct” way of writing inequalities
4 5 6
x5

34. The “correct” way of writing inequalities
4 5 6
x5
NOT 5  x

35. The “correct” way of writing inequalities
4 5 6 4 5 6
x5
NOT 5  x

36. The “correct” way of writing inequalities
4 5 6 4 5 6
x5 4 x6
NOT 5  x

37. The “correct” way of writing inequalities
4 5 6 4 5 6
x5 4 x6
NOT 5  x NOT 6  x  4

38. The “correct” way of writing inequalities
4 5 6 4 5 6
x5 4 x6
NOT 5  x NOT 6  x  4
NOT x  4 or x  6

39. The “correct” way of writing inequalities
4 5 6 4 5 6
x5 4 x6
NOT 5  x NOT 6  x  4
NOT x  4 or x  6
4 5 6

40. The “correct” way of writing inequalities
4 5 6 4 5 6
x5 4 x6
NOT 5  x NOT 6  x  4
NOT x  4 or x  6
4 5 6
x  4 or x  6

41. The “correct” way of writing inequalities
4 5 6 4 5 6
x5 4 x6
NOT 5  x NOT 6  x  4
NOT x  4 or x  6
4 5 6
x  4 or x  6
NOT x  6 or x  4

42. The “correct” way of writing inequalities
4 5 6 4 5 6
x5 4 x6
NOT 5  x NOT 6  x  4
NOT x  4 or x  6
4 5 6
x  4 or x  6
NOT x  6 or x  4
NOT 4  x  6

43. The “correct” way of writing inequalities
4 5 6 4 5 6
x5 4 x6
NOT 5  x NOT 6  x  4
NOT x  4 or x  6
Exercise 1F; 3acdijm, 4afkp,
4 5 6 5behlp, 6acf, 7bcegh, 8aceg,
x  4 or x  6 9bdfhj, 10a, 11*
NOT x  6 or x  4
NOT 4  x  6