[solving equations part 2][section 11]

(1.)  7x - 3x = 8            here is the problem

4x = 8               combine like terms
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4    4             divide each side by 4

x = 2           divide and cancel

result:  x = 2

(2.)   15 = 7x - 2x             here is the problem

15 = 5x             combine like terms
__  ___
5     5     divide each side by 5

3 = x          divide and cancel

result:  x = 3

(3.)   2(x - 5) = 4            here is the problem

2x - 10 = 4           multiply thru parentheses

+10 +10           add 10 to each side
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2          2           divide each side by 2

x = 7                   divide and cancel

result:  x = 7

(4.)   2x + 3(x + 5) = 0          here is the problem

2x + 3x + 15 = 0        multiply thru parentheses

5x + 15 = 0         combine like terms

-15  -15      subtract 15 from each side
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5x       = -15      subtract
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5           5       divide each side by 5

x = -3               divide and cancel

result:  x = -3

(5.)  -7b + 4(2b - 3) = 16           here is the problem

-7b + 8b - 12 = 16            multiply thru parentheses

b - 12 = 16            combine like terms

+ 12  +12        add 12 to each side
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result:  b = 28

(6.)  2b + 4(b - 6) = 12          here is the problem

2b + 4b - 24 = 12        multiply thru  parentheses

6b - 24 = 12           combine like terms

+24  +24           add 24 to each side
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6     6        divide each side by 6

b = 6            divide and cancel

result:  b = 6

(7.)  x - 4(3 - x) = 0           here is the problem

x - 12 + 4x = 0      multiply thru parentheses

5x - 12 = 0            combine like terms

+ 12  +12            add 12 to each side
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___         ___
5         5          divide each side by 5

x = 2.4              divide and cancel

result:  x = 2.4

(8.)    -4(x - 9) + 5 = 1           here is the problem

-4x + 36 + 5 = 1          multiply thru parentheses

-4x + 41 = 1         combine like terms

4x - 41 = -1      multiply thru by -1

+ 41  +41      add 41 to each side
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___       ____
4          4        divide each side by 4

x = 10            divide and cancel

result:  x = 10

(9.)   6 - (m - 4) = 18           here is the problem

6 - m + 4 = 18           multiply thru parentheses

10 - m = 18               combine like terms

-10 + m = -18           multiply thru by -1

+  10          + 10        add 10 to each side
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result:  m = -8

(10.)  -8 - (9 - 4m) = 15           here is the problem

-8 - 9 + 4m = 15        multiply thru parentheses

4m - 17 = 15          combine like terms

+    17  +17         add 17 to each side
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