Solve each formula for the indicated variable.

See Problem 5.

33. A = 1 2 b h , eh equals , 1 half , b h comma  for h
34. s = 1 2 g t 2 , s equals , 1 half , g , t squared , comma  for g
35. V = lwh, for w
36. I = prt, for r

Solve each equation for x.

37. ax + bx = c
38. x a − 5 = b x over eh , minus 5 equals b
39. x − 2 2 = m + n fraction x minus 2 , over 2 end fraction . equals m plus n
40. 2 5 ( x + 1 ) = g 2 fifths . open , x plus 1 , close . equals g

B Apply

Solve each equation.

41. 0.2 ( x + 3 ) − 4 ( 2 x − 3 ) = 0.9 0.2 open x plus 3 close minus 4 open 2 x minus 3 close equals 0.9
42. 12 − 3 ( 2 w + 1 ) = 7 w − 3 ( 7 + w ) 12 minus 3 open 2 w plus 1 close equals 7 w minus 3 open 7 plus w close
43. ( m − 2 ) − 5 = 8 − 2 ( m − 4 ) open m minus 2 close minus 5 equals 8 minus 2 open m minus 4 close
44. 7 ( a + 1 ) − 3 a = 5 + 4 ( 2 a − 1 ) 7 open eh plus 1 close minus 3 eh equals 5 plus 4 open 2 eh minus 1 close
45. Think About a Plan The measures of an angle and its complement differ by 22°. What are the measures of the angles?
    • What is true about the sum of the measures of an angle and its complement?
    • When modeling the problem with an equation, how can you algebraically represent that the two angle measures differ by 22°?

Solve each formula for the indicated variable.

46. R ( r 1 + r 2 ) = r 1 r 2 ,  for  R r open , r sub 1 , plus , r sub 2 , close equals , r sub 1 , r sub 2 , comma , for r
47. A = 1 2 h ( b 1 + b 2 ) , eh equals , 1 half , h . open . b sub 1 , plus , b sub 2 . close . comma  for b 2 b sub 2
48. s = 2 π r 2 + 2 π r h , s equals 2 pi , r squared , plus 2 pi r h comma  for h
49. h = v t = 5 t 2 , h equals v t equals 5 , t squared , comma  for v
50. v = s 2 + 1 2 s h , v equals , s squared , plus , 1 half , s h comma  for h
51. R ( r 1 + r 2 ) = r 1 r 2 ,  for  r 2 r open , r sub 1 , plus , r sub 2 , close equals , r sub 1 , r sub 2 , comma , for , r sub 2
52. Writing Suppose you write and solve an equation to determine the amount of money m you have in your bank account after several weeks. You find that m = − 36 . m equals negative 36 .  What does this solution mean?
53. Geometry The measure of the supplement of an angle is 20° more than three times the measure of the original angle. Find the measures of the angles.
54. Find 4 consecutive odd integers with a sum of 184.

Solve each equation for x.

55. c ( x + 2 ) − 5 = b ( x − 3 ) c open x plus 2 close minus 5 equals b open x minus 3 close
56. a ( 3 t x − 2 b ) = c ( d x − 2 ) eh open 3 t x minus 2 b close equals c open d x minus 2 close
57. b ( 5 p x − 3 c ) = a ( q x − 4 ) b open 5 p x minus 3 c close equals eh open q x minus 4 close
58. a b ( 2 x − 12 ) = c d eh over b . open . 2 x minus 12 . close . equals , c over d
59. 3 a x 5 − 4 c = a x 5 fraction 3 eh x , over 5 end fraction . minus 4 c equals , fraction eh x , over 5 end fraction
60. a − c x − a = m fraction eh minus c , over x minus eh end fraction . equals m

Write an equation to solve each problem.

61. Swimming A city park is opening a new swimming pool. You can pay a daily entrance fee of $3 or purchase a membership for the 12-week summer season for $82 and pay only $1 per day to swim. How many days would you have to swim to make the membership worthwhile?
62. Rocket The first stage of a rocket burns 28 s longer than the second stage. If the total burning time for both stages is 152 s, how long does each stage burn?
63. Error Analysis Your friend says that the equations shown are two ways to write the same formula. Is your friend correct? Explain your answer.

    

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