Solve each equation. Check your answers.

46. x − 6 x + 3 + 2 x x − 3 = 4 x + 3 x + 3 fraction x minus 6 , over x plus 3 end fraction . plus . fraction 2 x , over x minus 3 end fraction . equals . fraction 4 x plus 3 , over x plus 3 end fraction
47. n n − 2 + n n + 2 = n n 2 − 4 fraction n , over n minus 2 end fraction . plus . fraction n , over n plus 2 end fraction . equals . fraction n , over n squared , minus 4 end fraction
48. 2 r + 1 r 2 = r 2 + r r 3 = 1 r 2 over r , plus , fraction 1 , over r squared end fraction , equals . fraction r squared , plus r , over r cubed end fraction . equals , 1 over r
49. 3 t − t 2 − 2 t t 3 = 4 t 2 3 over t , minus . fraction t squared , minus 2 t , over t cubed end fraction . equals , fraction 4 , over t squared end fraction
50. Painting To paint a room, it takes Mike 75 min, Joan 60 min, and Kyle 80 min when each person works alone. If all three work together, how long will the painting take?
51. Window Washing Sumi can wash the windows of an office building in 3 4 3 fourths  the time it takes her apprentice. One day they worked on a building together for 2 h 16 min, and then Sumi continued alone. It took her 4 h 32 min more to complete the job. How long would it take her apprentice to wash all the windows alone?

Standardized Test Prep

SAT/ACT

52. Which inequality contains both solutions of x = 1 2 + 3 x ? x equals , 1 half , plus , 3 over x . question mark
    1. − 1 < x < 3 negative 1 less than x less than 3
    2. − 2 < x ≤ 2 negative 2 less than x less than or equal to 2
    3. − 2 ≤ x < 0 negative 2 less than or equal to x less than 0
    4. − 3 ≤ x ≤ − 1 negative 3 less than or equal to x less than or equal to negative 1
53. Which expression is equivalent to 4 x + 3 2 x − 6 x 2 − 9 ? fraction fraction 4 , over x plus 3 end fraction , over fraction 2 x minus 6 , over x squared , minus 9 end fraction end fraction . question mark
    6. 2
    7. − 2 negative 2
    8. 8 x 2 + 6 x + 9 fraction 8 , over x squared , plus 6 x plus 9 end fraction
    9. 2 x + 6 x − 3 fraction 2 x plus 6 , over x minus 3 end fraction
54. Which is the least common denominator of 1 x , x 3 , 1 over x , comma , x over 3 , comma  and 3 2 x ? fraction 3 , over 2 x end fraction , question mark
    1. 2x
    2. 3x
    3. 6x
    4. 6 x 2 6 , x squared

Short Response

55. A grizzly bear can run as fast as 30 mi/h. At that rate, how many feet would a grizzly bear travel in 1 s? Explain your answer.

Mixed Review

See Lesson 11-4

Add or subtract.

56. 5 x 2 y 2 z − 8 x 2 y 2 z fraction 5 , over x squared , y squared , z end fraction . minus . fraction 8 , over x squared , y squared , z end fraction
57. 3 h 2 2 t 2 − 8 + h t − 2 fraction 3 , h squared , over 2 , t squared , minus 8 end fraction . plus . fraction h , over t minus 2 end fraction
58. k − 11 k 2 + 6 k − 40 − 5 k − 4 fraction k minus 11 , over k squared , plus 6 k minus 40 end fraction . minus . fraction 5 , over k minus 4 end fraction

See Lesson 10-5.

Graph each function, either by translating the graph of y = x y equals square root of x  or by making a table of values.

59. f ( x ) = − 2 x f open x close equals negative 2 square root of x
60. y = x + 7 y equals , square root of x plus 7 end root
61. f ( x ) = x − 2 − 8 f open x close equals , square root of x minus 2 end root , minus 8
62. y = 0.25 x y equals , square root of 0.25 , x end root

Get Ready! To prepare for Lesson 11-6, do Exercises 63–66.

See Lesson 5-2.

Determine whether each equation represents a direct variation. If it does, find the constant of variation.

63. y − 3 x = 0 y minus 3 x equals 0
64. y + 7 = x y plus 7 equals x
65. x + 4 y + 1 = 1 x plus 4 y plus 1 equals 1
66. 8 x = 3 y 8 x equals 3 y

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