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Equations/Inequations
Equations/Inequations
   Make the pronumeral the subject of the formula
Equations/Inequations
               Make the pronumeral the subject of the formula
e.g. (i ) x  3  6
Equations/Inequations
               Make the pronumeral the subject of the formula
e.g. (i ) x  3  6
Equations/Inequations
             Make the pronumeral the subject of the formula
e.g. (i ) x  3  6
              x  63
              x3
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
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
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
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
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
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
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
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
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
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
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
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
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
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
The inequality sign will only change when:
The inequality sign will only change when:
1) Multiply or divide by a negative number
  “if you change the sign, you change the sign”
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
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
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
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
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
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
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
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
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
The “correct” way of writing inequalities
The “correct” way of writing inequalities


4   5     6
The “correct” way of writing inequalities


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


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


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


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


  4   5   6                          4  5    6
    x5                              4 x6
NOT 5  x                        NOT 6  x  4
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
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
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
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
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
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

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MakePronumeralSubjectFormula

  • 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