[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