[solving equations][section 9]

(1.)  5n + 3 = 33                        here is the problem

          -3   -3       subtract 3 from each side
     _______________
      5n     = 30        subtract
     ____     ___
       5       5     divide each side by 5

         n = 6          divide and cancel

result:  n = 6

(2.)   2n + 3 = 7               here is the problem

           -3   -3          subtract 3 from each side
       _____________
        2n   =   4           subtract
        ___      __
         2       2           divide each side by 2

          n = 2             divide and cancel

result:  n = 2

(3.)  5n - 3 = 17            here is the problem

        +  3  + 3          add 3 to each side
     _____________
       5n =   20          add
       ___  _____
       5       5       divide each side by 5

         n = 4          divide and cancel

result:  n = 4

(4.)  3t + 17 = 5                 here is the problem

          -17  -17      subtract 17 from each side
      ______________
      3t   =   -12              subtract
     ___        ___
      3          3     divide each side by 3

          t = -4          divide and cancel

result:  t = -4

(5.)  2a + 15 = 3            here is the problem

          -15  -15          subtract 15 from each side
     _______________
      2a   =  -12           subtract
     ____      ___
       2        2         divide each side by 2

           a = -6            divide and cancel

result:  a = -6

(6.)  3n - 17 = 4              here is the problem

          +17  +17             add 17 to each side
     _______________
       3n   =  21               add
       ___     ___
        3        3     divide each side by 3

           n = 7        divide and cancel

result:  n = 7

(7.)  9a - 1 = 80                here is the problem

        +  1  + 1            add 1 to each side
    ________________
      9a   =   81             add
      ___      ___
      9         9          divide each side by 9

          a = 9            divide and cancel

result:  a = 9

(8.)  5 - 3a = 32

    -5 + 3a = -32            multiply thru by -1

  +  5        + 5             add 5 to each side
    ________________
       3a = -27               add
      ____  ____
        3      3              divide each side by 3

          a = -9          divide and cancel

result:   a = -9

(9.)   5 - 2y = 15             here is the problem

      -5 + 2y = -15          multiply thru by -1

   +   5        + 5      add 5 to each side
   _________________
           2y = -10        add
         _____  ______
            2      2         divide each side by 2

                y = -5           divide and cancel

result:   y = -5

(10.)  7 = 6x + 19               here is the problem
  
       6x + 19 = 7        rearrange like this

           -19  -19        subtract 19 from each side
     ___________________
      6x       = -12          subtract
    _______     ______
        6        6              divide each side by 6

         x = -2                 divide and cancel

result:  x = -2

(11.)   8 = 5y + 33

     5y + 33 = 8          rearrange like this

         -33  -33        subtract 33 from each side
    _________________
     5y    = -25        subtract
     ___     ____
      5        5         divide each side by 5

          y = -5           divide and cancel

result:  y = -5

(12.)  -5 = 32 - 3b             here is the problem

      32 - 3b = -5           rearrange like this

     -32 + 3b = 5           multiply thru by -1

   +  32      + 32           add 32 to each side
     _________________
          3b = 37             add
          ___  ___
          3     3       divide each side by 3

        b = 12 1/3         change to mixed number, and cancel

result:  b = 12 1/3

(13.)   4 = 30 - 6t             here is the problem

     30 - 6t = 4             rearrange like this

     -30 + 6t = -4                  multiply thru by -1

   +30     +   30        add 30 to each side
   ___________________
          6t = 26             add
          ___  ___
          6     6             divide each side by 6

          t = 13/3         reduce and cancel

          t = 4 1/3          write as a mixed number

result:  t =  4 1/3

(14.)  15 - (5/4)v = 23          here is the problem

      -15 + (5/4)v = -23         multiply thru by -1
 

   +  15          +  15        add 15 to each side
   ________________________
          (5/4)v =  -8             add

       (4/5)(5/4)v = (-8)(4/5)   multiply each side by 4/5

                v = -32/5         cancel and multiply

             v = -6.4              divide

result:  v = -6.4

(15.)    6 = 26 + (2/5)n

      26 + (2/5)n = 6            rearrange like this

      -26         -26      subtract 26 from each side
    _____________________
        (2/5)n = -20            subtract

   (5/2)(2/5)n = (-20)(5/2)   multiply each side by 5/2

           n = -50         cancel and multiply

result:  n = -50

(16.)   0 = (7/10)n - 35         here is the problem

      + 35          + 35     add 35 to each side
    _________________________
       35 = (7/10)n              add

    10*35 = 10(7/10)n         multiply each side by 10

         350 = 7n                multiply and cancel
        _____ ____
           7   7            divide each side by 7

       50 = n               divide and cancel

result:  n = 50

(17.)   (2/3)t - 13 = 57              here is the problem

               + 13  +13         add 13 to each side
      ______________________
      (2/3)t       = 70          add
   
    (3/2)(2/3)t = (3/2)(70)    multiply each side by 3/2

             t = 105       multiply and cancel

result:  t = 105 

  

(18.)  49 + (3/5)x = 16            here is the problem

     -49          -49    subtract 49 from each side
    ________________________
             (3/5)x = -33      subtract

          (5/3)(3/5)x = (-33)(5/3)    multiply ea side by 5/3

               x = -55          multiply and cancel

result:  x = -55

(19.)   0 = 0.6n - 3.6          here is the problem

 +   3.6        +  3.6      add 3.6 to each side
   ______________________
    3.6 = 0.6n                  add
    ____  ____
   0.6     0.6                 divide each side by 0.6

       6 = n                  divide and cancel

result: n = 6

(20.)  (3/4)x - 3 = 18               here is the problem

               +3  +3          add 3 to each side
    ______________________
        (3/4)x  =  21          add

       (4/3)(3/4)x = (4/3)(21)   multiply each side by 4/3

              x = 28              multiply and cancel

result:  x = 28