College Algebra 9th txtbk

SECTION 1–6 Additional Equation-Solving Techniques 103
7. (x 5) 2 x 2 25 8. (2x 1) 2 4x 2 1
59. t 111t 18 0 60. x 15 21x
9. (1x 1 1) 2 x 10. (1x 1) 2 1 x
11. If x 3 2, then x 8. 12. If x 13 8, then x 2.
In Problems 13–26, solve the equation.
13. 1x 2 4
14. 1x 4 2
15. 13y 5 10 0 16. 14 x 5 0
17. 13y 2 y 2 18. 14y 1 5 y
19. 15w 6 w 2 20. 12w 3 w 1
21. 2x 1 x 2 22. 2x 2 5 x
23. x 5 7 2x 24. x 7 1 2x
25. 3x 4 2x 5 26. 3x 1 x 1
In Problems 27–32, transform each equation of quadratic type
into a quadratic equation in u and state the substitution used in
the transformation. If the equation is not an equation of quadratic
type, say so.
4
27. 28.
7 3 x 6
2x6 4x 3 0
x 0 2
29. 3x 3 4x 9 0 30. 7x 1 3x 1/2 2 0
10
31. 32. 3x 3/2 5x 1/2 12 0
9 4 x 7 2 x 0 4
In Problems 33–56, solve the equation.
33. 13t 2 1 21t 34. 15t 4 21t 1
35. m 4 2m 2 15 0 36. m 4 4m 2 12 0
37. 3x 2x 2 2
38. x 25x 2 9
39. 2y 23 5y 13 12 0 40. 3y 23 2y 13 8 0
41. (m 2 2m) 2 2(m 2 2m) 15
42. (m 2 2m) 2 6(m 2 2m) 16
43. 12t 3 2 1t 2
44. 12x 1 1x 5 3
45. 1w 3 12 w 3
46. 1w 7 2 13 w
47. 18 z 1 1z 5
48. 13z 1 2 1z 1
49. 24x 2 12x 1 6x 9
50. 6x 24x 2 20x 17 15
51. y 2 2y 1 3 0 52. y 2 3y 1 4 0
53. 2t 4 5t 2 2 0 54. 15t 4 23t 2 4 0
55. 3z 1 3z 1/2 1 0 56. 2z 1 3z 1/2 2 0
In Problems 61–68, solve the equation.
61. 17 2x 1x 2 1x 5
62. 11 3x 12x 1 1x 2
63. 3 x 4 5x 2
64. 2 4x 4 7x 2
65. 21x 5 0.01x 2.04
66. 31x 1 0.05x 2.9
67. 2x 25 5x 15 1 0
68. x 25 3x 15 1 0
69. Explain why the following “solution” is incorrect:
70. Explain why the following “solution” is incorrect.
APPLICATIONS
1x 3 5 12
x 3 25 144
2x 2 16 2x 3
x 4 2x 3
7 x
x 116
71. PHYSICS—WELL DEPTH When a stone is dropped into a deep
well, the number of seconds until the sound of a splash is heard is
given by the formula t 1x where x is the depth of the
4 x
1,100 ,
well in feet. For one particular well, the splash is heard 14 seconds
after the stone is released. How deep (to the nearest foot) is the well?
72. PHYSICS—WELL DEPTH Refer to Problem 71. For a different
well, the sound of the splash is heard 2 seconds after the stone is released.
How deep (to the nearest foot) is the well?
73. GEOMETRY The diagonal of a rectangle is 10 inches and the
area is 45 square inches. Find the dimensions of the rectangle, correct
to one decimal place.
74. GEOMETRY The hypotenuse of a right triangle is 12 inches and
the area is 24 square inches. Find the dimensions of the triangle,
correct to one decimal place.
75. MANUFACTURING A lumber mill cuts rectangular beams from
circular logs (see the figure). If the diameter of the log is 16 inches
and the cross-sectional area of the beam is 120 square inches, find
the dimensions of the cross section of the beam correct to one decimal
place.
Solve Problems 57–60 two ways: by squaring and by substitution.
57. m 71m 12 0 58. y 6 1y 0