[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
_____________
___  _____
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
_______________
___     ___
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
________________
___      ___
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
________________
____  ____
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
_________________
_____  ______
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
_________________
___  ___
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
___________________
___  ___
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
________________________

(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
_________________________

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
______________________

(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
______________________
____  ____
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
______________________