[solving equations for a variable][section 18]

(1.) C = ∏d         solve for d

C = ∏d             here is the problem
___  ___

divide each side by ∏

C/∏ = d               cancel

result:  d = C/∏

(2.)  A = bh       solve for b

A = bh             here is the problem
___  ___
h    h        divide each side by h

A/h = b            cancel

result:  b = A/h

(3.)   P = 2L + 2w      solve for w

-2L -2L         subtract 2L from each side
_______________
P - 2L =   2w          subtract
______   _____
2       2        divide each side by 2

(P - 2L)/2 = w            cancel

result:  w = (P - 2L)/2

(4.)  A = (1/2)bh       solve for h

A = (1/2)bh             here is the problem

2* A = 2*(1/2)bh     multiply each side by 2

2A = bh              cancel
___ ____
b    b            divide each side by b

2A/b = h             cancel

result:  h = 2A/b

(5.)  i = prt     solve for t

i = prt          here is the problem
___ _____
pr   pr         divide each side by pr

i
____ = t             cancel
pr
i
result:     t = _______
pr

(6.)  C = (5/9)(F - 32)   solve for F

(9/5)C = (9/5)(5/9)(F - 32)     multiply each side by 9/5

(9/5)C = F - 32                   cancel

+ 32       + 32           add 32 to each side
____________________
(9/5)C + 32 = F             add

result:  F = (9/5)C + 32

(7.)   a + b + c = 180         solve for b

-a          - a       subtract a from each side
________________________
b + c = 180 - a        subtract

-c         - c   subtract c from each side
_________________________
b    = 180 - a - c     subtract

result:  b = 180 - a - c

(8.)   2n + 5a = 8a     solve for n

-5a  -5a      subtract 5a from each side
___________________
2n  =     3a       subtractS
____      ____
2          2      divide each side by 2

3a
n = ______             cancel
2

3a
result:   n = ______
2

(9.)    a(b + n) = c     solve for b

a(b + n) = c             here is the problem

ab + an = c           multiply thru parentheses

-an   - an        subtract an from each side
____________________
ab       = c - an        subtract
_____       ________
a            a        divide each side by a

b = (c - an)/a            cancel

result:  b = (c - an)/a

(10.)   A = (1/2)h(b1 + b2)      solve for b1

A = (1/2)h(b1 + b2)      here is the problem

2A = 2(1/2)h(b1 + b2)       multiply each side by 2

2A = h(b1 + b2)              cancel
__   _________
h       h                divide each side by h

2A/h = b1 + b2                  cancel

-b2    - b2        subtract b2 from each side
_____________________
(2A/h) - b2 = b1                 subtract

result:  b1 = (2A/h) - b2