By Richard N. Aufmann

Includes entire recommendations to all odd-numbered difficulties within the textual content, in addition to learn suggestions and a convention checks for every bankruptcy; textual content particular.

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**Extra resources for Instructor’s Solutions Manual of College Algebra And Trigonometry **

**Sample text**

X+4 = x+4 ax + b = cx + d ax − cx = d − b x(a − c) = d − b x = d −b, a −c ≠ 0 a−c x −1 = x −1 if x − 1 ≥ 0 if x + 4 < 0 x < −4 x ≥1 x −1 = x −1 x + 4 = − ( x + 4) x + 4 = −x − 4 2 x = −8 x = −4 an identity if x − 1 < 0 x <1 x − 1 = −( x − 1) x −1 = −x + 1 2x = 2 x =1 The case x + 4 < 0 has no solution since there is no real number x such that x < − 4 and x = − 4. The case x −1 < 0 has no solution since there is no real number x such that x < 1 and x = 1. {x | x ≥ −4} {x | x ≥ 1} 64. x + 7 = −( x + 7) if x + 7 ≥ 0 x ≥ −7 x + 7 = −( x + 7) x + 7 = −x − 7 2 x = −14 x = −7 {x | x ≤ −7} if x + 7 < 0 x < −7 x+7 = x+7 an identity x − 3 = −( x − 3) if x − 3 ≥ 0 x≥3 x − 3 = −( x − 3) x − 3 = −x + 3 2x = 6 x=3 {x | x ≤ 3} Copyright © Houghton Mifflin Company.

5 13. 5 17. 14. Let x = the number 1 1 1 x + x = x −5 5 4 2 1 ⎞ ⎛1 ⎛1 ⎞ 20⎜ x + x ⎟ = 20⎜ x − 5 ⎟ 5 4 2 ⎝ ⎠ ⎝ ⎠ 4 x + 5 x = 10 x − 100 9 x = 10 x − 100 100 = x 15. 2 18. 1) The original fraction is x−4 . 2 W P = 2 L + 2W 174 = 2(2W − 3) + 2W 174 = 4W − 6 + 2W 180 = 6W W = 30 ft L = 2W − 3 = 2(30) − 3 = 60 − 3 = 57 ft x + 10 = 5 x − 50 − 4 x = −60 The original fraction is 15 − 4 11 = . 15 15 21. 22. 110 = 2 L + 2 ⎡ 1 L + 1⎤ ⎣2 ⎦ 110 = 2 L + L + 2 108 = 3L L = 36 m W = 1 L + 1 = 1 (36) + 1 2 3x + 3 x + x = 84 7 x = 84 x = 12 3 x = 3(12) = 36 The shortest side is 12 cm.

An − a1 = ( n − 1)d an − a1 =d n −1 2 A − hb2 = b1 h 9. A = P + Pr t A = P(1 + rt ) 4. 2 A − hb2 = hb1 2 8. 3. 10. P1V1 P2V 2 = T1 T2 P1V1T2 = P2V 2T1 P1V1T2 = V2 P2T1 Copyright © Houghton Mifflin Company. All rights reserved. 2 41 11. 8 12. 5 13. 5 17. 14. Let x = the number 1 1 1 x + x = x −5 5 4 2 1 ⎞ ⎛1 ⎛1 ⎞ 20⎜ x + x ⎟ = 20⎜ x − 5 ⎟ 5 4 2 ⎝ ⎠ ⎝ ⎠ 4 x + 5 x = 10 x − 100 9 x = 10 x − 100 100 = x 15. 2 18. 1) The original fraction is x−4 . 2 W P = 2 L + 2W 174 = 2(2W − 3) + 2W 174 = 4W − 6 + 2W 180 = 6W W = 30 ft L = 2W − 3 = 2(30) − 3 = 60 − 3 = 57 ft x + 10 = 5 x − 50 − 4 x = −60 The original fraction is 15 − 4 11 = .