Page 39 - WCS - Electrical
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              28+  =  + 7                          28+
             + 4                                  + 4  = + 7
             + 56  =  − 14                        + 56
              - 4                                  - 4  = − 14
             - 72  =  −8              28+  = + 7  - 72
                                       4
             + 9                     + + 56       + 9  =  −8
             − 96                        = − 14   − 96
                 =
                   +16
                                                        +16
                                                      =
                                      -
                                       4
           5 is transposed from left side to the right side by changing its sign from + to –.
             − 6
                                                  − 6
             5y   20                 - 72  =  −8  5y   20
                =
                                                     =
                                     +
                                       9
                    = 20.  Multiply both sides by 4.  Then       x 4  = 20 x 4.
                  5
             5
                                                  5
                                                       5
                                     − 96
             x                           =  +16   x
                                     − 6

                4                    5y  20  x  = 80,
                                                  4
             5x  =  25                  =         5x  25
             5    5                  x 5  5  5x = 25. =  5
                                                  5
             10a
           Divide both sides by 5 then            10a
                                     4
             2a                      5x  25       2a
             −  8ac                  5  =  5  x = 5. −  8ac
              2bc
                                                   2bc
                                     10a
                        7p
                    6n −
              5m −×
             − When transposing numbers or letter symbols from one side to the other side multiplication becomes
                                                             7p
                                                   5m −×
                                                         6n −
                                                  −
                                     2a
                  28mn
                −
                                                     −
                                                       28mn
              division and the division becomes multiplication.
                                      8ac
             5a + 20                 −            5a + 20
              The equality of an equation remains unchanged when both sides of the equation are treated in the
             7a + 28                 − 2bc  6n − 7p 7a + 28
                                      5m −×
              m
                                                   m
             a same way.  When transposing from one side to the other side,
                                                  a
                      n
                   m−
                                                        m−
                                                           n
                                        −
                                          28mn
                  a
                =
                                                       a
              n
                                         20
                                     5a +
             a a plus quantity becomes minus quantity. n  =
                                                  a
              3
                                                   3
                                     7a +
                                         28
             2 a minus quantity becomes a plus quantity =  2 − 2 = 2 = 2
                                                  2
                   3
                          1
                                                               1
                                                        3
                         2 =
                             2
                      2 =
                  2 −
                =
                                      m
             2 2                     a  = a m− n  2 2
              a multiplication becomes a division
             2× 2× 2  =  8  = 2      a n          2× 2× 2  8
                                      3
                 2
                      4
              2×
                                     2
              a division becomes a multiplication.  1 2× 2  =  4  =  2
                                           3
                                                   n
             a n   a  n             2  = 2 − 2 =  2 =  2  a  n
                                                  a
                                     2
              To solve simple equations isolate the unknown quantity which is to be found on the left side of the
                =
                    
                 
                                                     =
                                                      
                                                         
                 
              n
                  b 
             b equation.             2× 2× 2  =  8  =  b 2  n    b 
             2 3  =   2   2  =  2× 2  =  4  n 2× 2  n  4  2 3   2  2  2× 2  4
              2
           Example 3    3× 3  9     a n  =    a    3 2  =    3    =  3× 3  =  9
                  
             3
                                          b 
                   1
                                     b
              −
               n
           •  Solve for x if 4x = 3(35 – x ) 3    2  2  2× − 2 n  = 4 1
             a
                 =
                                                  a
                    n
                                     2
                                          
                  a
                                          
                                        =
              4x  = 105 – 3x  (brackets removed)   =  =  a 1 n
                   1
                                      2
               2
              −
             2   =                   3     3   3 2 − ×  2 3  = 9
                    2
                                                         2
                                           1
              4x  + 3x  = 105 (By transposing –3x  on the right side to the left side)
                   2
                                       n
                                      −
                                                       2
                                    a
                                         =
                        2
                 2
               3 
                                                    3 
              7x = 105
                1   =   7      − 2  a 1 n    1  2  =    7   2
                                         =
                    
                                     2
               4 
                      4 
                                                         
               7 x = 15 (dividing both sides by 7) 2   7  4  7  49 4 
                7
                    49
                                          2
             4 ×  4  =  16            3  2    7  2  4  ×  4  =  16
                                     1   =    
                                      4     4 
                                     7  ×  7  =  49
                                     4  4   16
                                                           26
                                            CITS : WCS - Electrical - Exercise 4
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