[solving equations part 3][section 15]

(1.)   5x = 2x + 12             here is the problem

-2x  -2x        subtract 2x from each side
___________________
3x =       12     subtract
___        ___
3          3        divide each side by 3

x = 4                divide and cancel

result:  x = 4

(2.)  7y + 8 = 11y          here is the problem

11y = 7y + 8          rearrange like this

-7y  -7y          subtract 7y from each side
_________________
4y =      8        subtract
_____   _______
4        4          divide each side by 4

y = 2             divide and cancel

result:  y = 2

(3.)   -7m = 9m - 12               here is the problem

7m = -9m + 12      multiply thru by -1

+  9m    +9m         add 9m to each side
_____________________
____        ___
16           16      divide each side by 16

m = 3/4     reduce and cancel

result:  m = 3/4

(4.)  4a - 5 = 7a - 7            here is the problem

-4a + 5 = -7a + 7            multiply thru by -1

+7a      + 7a           add 7a to each side
_______________________
3a + 5 =        7   add

-5         -5         subtract 5 from each side
_______________________
3a           =  2         subtract
___          ______
3               3       divide each side by 3

a = 2/3             cancel

result:  a = 2/3

(5.)   -6x - 7 = -5x + 3             here is the problem

6x + 7 = 5x - 3         multiply thru by -1

-5x     -5x          subtract 5x from each side
_________________________
x + 7 =     -3            subtract

-7       -7         subtract 7 from each side
____________________
x      =   -10        subtract

result: x = -10

(6.)   -3r - 8 = -5r + 12             here is the problem

+   5r     + 5r             add 5r to each side
_________________________
2r - 8 =      12         add

+ 8    +  8    add 8 to each side
________________________
___        ___
2           2         divide each side by 2

r = 10           divide and cancel

result:  r = 10

(7.)   q + 7q = -12q + 10           here is the problem

8q = -12q + 10            combine like terms

+ 12q  +12q             add 12q to each side
_____________________
_____         _____
20           20          divide each side by 20

q = 1/2           reduce and cancel

result:  q = 1/2

(8.)   4(x + 2) = 3x              here is the problem

4x + 8 = 3x                multiply thru parentheses

-8      -8         subtract 8 from each side
__________________
4x   = 3x - 8               subtract

-3x     -3x           subtract 3x from each side
_____________________
x  =      -8       subtract

result:  x = -8

(9.)   5(m - 5) = 3(m + 1)             here is the problem

5m - 25 = 3m + 3      multiply thru parentheses

+  25      + 25     add 25 to each side
________________________

5m     =  3m + 28         add

-3m         -3m        subtract 3m from each side
__________________________
2m     =        28      subtract
___             ___
2               2      divide each side by 2

m = 14          divide and cancel

result:  m = 14

(10.)   7y = -2(y + 9)                here is the problem

7y = -2y - 18          multiply thru parentheses

+2y   +2y                add 2y to each side
_____________________
____     _____
9        9            divide each side by 9

y = -2                divide and cancel

result:  y = -2

(11.)   -4(a - 5) = -7(a - 2) + 6           here is the problem

-4a + 20 = -7a + 14 + 6     multiply thru parentheses

-4a + 20 = -7a + 20    combine like terms

+7a      + 7a           add 7a to each side
________________________
3a + 20 =      20         add

-20       -20     subtract 20 from each side
___________________________
3a       = 0                subtract
____       ____
3          3            divide each side by 3

a  = 0                   divide and cancel

result:  a = 0

(12.)  36 - 2(c - 28) = -4(2c + 52)       here is the problem

36 - 2c + 56 = -8c - 208     multiply thru

-2c + 92 = -8c - 208    combine like terms

+ 8c         + 8c          add 8c to each side
__________________________

6c + 92 =     -208           add

-92       -92         subtract 92 fr ea side
________________________
6c       =  -300          subtract
____          ____
6             6       divide each side by 6

c = -50            divide and cancel

result:  c = -50