Practice and Applications

  1. 7. x > 6

    A number line is shaded to the right of an open circle at 6.

  2. 9. 52 < x < 6

    A number line is shaded between open circles at 5 over 2 and 6.

  3. 11.  − 2 < x < 15  

    A number line is shaded between open circles at negative 2 and one-fifth.

  4. 13. n <  − 73 or n > 52

    A number line is shaded to the left of an open circle at negative seven-thirds, and to the right of an open circle at 5 over 2.

  5. 15. x <  − 4 ,  12 < x < 3

    A number line is shaded to the left of an open circle at negative 4, and between open circles at one-half and 3.

  6. 17. x < 0 ,  x > 4

    A number line is shaded to the left of an open circle at 0, and to the right of an open circle at 4.

  7. 19.  − 2 ≤ x ≤ 23 

    A number line is shaded between closed circles at negative 2 and two-thirds.

  8. 21. x <  − 45 ,  x > 2

    A number line is shaded to the left of an open circle at negative four-fifths, and to the right of an open circle at 2.

  9. 23. x < 53

    The calculator graph of a horizontal that goes to the left of (five-thirds, 1).

  10. 25. 2 ≤ n < 114

    The calculator graph of a horizontal line segment that goes from (2, 1) to (eleven-fourths, 1).

  11. 27. R <  − 12 ,  R ≥ 8

    The calculator graphs of horizontal lines that go to the left of (negative one-half, 1), and to the right of (8, 1).

  12. 29. x <  − 18 ,  x > 78

    The calculator graphs of horizontal lines that go to the left of (negative 18, 1), and to the right of (78, 1).

  13. 31. x <  − 0.68

    The calculator graph of a curve that rises and inflects through an open circle at (negative 0.68, 0). The x-axis is shaded to the left of negative 0.68.

  14. 33. t < 0.69

    The calculator graph of a curve that falls through an open circle at (0.69, 0) with decreasing steepness. The x-axis is shaded to the left of 0.69.

  15. 35.

    The graph of a dashed line that falls through (0, 12) and (4, 0). The area above the line is shaded.

  16. 37.

    The graph of a solid line that rises through (negative four-thirds, 0) and (0, 2). The area below the line is shaded.

  17. 39.

    The graph of a dashed line that falls through (0, 6) and (3, 0). The area above the line is shaded.

  18. 41.

    The graph of a dashed upward opening V-shape with a vertex at (negative 1, 0). The area below the shape is shaded.

  19. 43.

    The graphs of a dashed line that rises through (negative 1, 0) and (0, 1), and a dashed parabola that opens downward with a vertex at (0, 4). The area above the line and below the parabola is shaded.

  20. 45.

    The graphs of a solid curve that rises from the x-axis to the positive y-axis, then falls toward the x-axis, and a dashed line that rises through (0, negative 3) and (3, 0). The area below the curve and below the line is shaded.

  21. 47.

    The calculator graph of a line that rises through (negative five-thirds, 0) and (0, 5). The area below the line is shaded.

  22. 49.

    A parabola opens downward with a vertex in quadrant 1. The area above the parabola is shaded.

  23. 51.

    The calculator graph of a curve that rises through (0, 0) to (2, 49), then falls through (3, 0). The area below the curve is shaded. All data are approximate.

  24. 53.

    The calculator graphs of 2 curves.

  25. 55. x ≤ 4

  26. 57. x ≤  − 3 ,  x ≥ 0

  27. 59. Max P = 29 at (1, 3)

  28. 61. Min C = 658at (38 , 74)

  29. 63. a and b must have different signs.

  30. 65. x <  − 3 or x > 2

  31. 67. x2 − 2x − 15 < 0

  32. 69.

    A parabola opens upward with a vertex at (0, 0) and open circles on its ends in quadrants 2 and 1.

  33. 71.

    f(x) > 0 for x < 2 or x > 3f(x) < 0 for  2 < x < 3f(x) = 0 for x = 2 ,  x = 3f(0) = 6 ,  f(5) = 6

    A parabola opens upward, falling through (0, 6) and (2, 0), then rising through (3, 0).

  34. 73. No values satisfy both inequalities

  35. 75. 0 < x ≤ 8.0 cm

  36. 77. Between $5 and $12.50

  37. 79. d > 39.5 m

  38. 81. 168,000 ≤ B ≤ 400,000 Btu

  39. 83. 0.456 < i < 0.816 A

  40. 85. r > 5.7

  41. 87.

    The graph of a shaded rectangular area with vertices at (0, 0), (1200, 0), (0, 1000), and (1200, 1000).

  42. 89. 300 regular

    150 deluxe

    The graphs of 2 solid lines. One falls through (0, 300) and (300, 150), and the other falls through (300, 150) to (450, 0). The area below both lines and in quadrant 1 is shaded.

  43. (Max P = $4650)

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