College Algebra 9th txtbk

106 CHAPTER 1 EQUATIONS AND INEQUALITIES
CHAPTER
1 Review Exercises
Work through all the problems in this chapter review and check
answers in the back of the book. Answers to all review problems
are there, and following each answer is a number in italics
indicating the section in which that type of problem is discussed.
Where weaknesses show up, review appropriate sections in the
text.
In Problems 1–3, solve the equation.
1. 8x 10 4x 30
2. 4 3(x 2) 5x 7(4 x)
y 10
3. 1 15 5 y 1 1 6 10
Solve and graph the inequality in Problems 4–6.
4. 3(2 x) 2 2x 1 5. y 9 6 5
6. 3 2x 5
7. Find the real part, the imaginary part, and the conjugate:
(A) 9 4i (B) 5i (C) 10
8. Perform the indicated operations and write the answer in standard
form.
(A) (4 7i) (2 3i)
(B) (3 5i) (4 8i)
(C) (1 2i)(3 4i)
21 9i
(D)
5 2i
Solve the equation in Problems 9–15.
9. 2x 2 7 0
10. 5x 2 20 0
11. 2x 2 4x
12. 2x 2 7x 3
13. m 2 m 1 0 14. y 2 3 2 ( y 1)
15. 15x 6 x 0
16. For what values of x does the expression 115 6x represent
a real number?
Solve the equation in Problems 17 and 18.
7 10 4x u 3
17. 18.
2u 2 1 6 1 u
2 x x 2 3x 10
3u 3
Solve and graph the inequality in Problems 19–21.
x 3
19. 5 2 x 20. 3x 8 7 2
8
3
21. 2(1 2m) 2 3
[
1 2
[
m
22. If points A, B, and C have coordinates on a number line of 5, 20,
and 8 respectively, find
(A) d(A, B) (B) d(A, C) (C) d(B, C)
23. Perform the indicated operations and write the final answers in
standard form:
(A) (3 i) 2 2(3 i) 3 (B) i 27
24. Convert to a bi forms, perform the indicated operations, and
write the final answers in standard form:
(A) (2 14) (3 19)
2 11 4 125
(B)
(C)
3 14 14
Solve the equation in Problems 25–30.
25. ay 11 2
3 b 20
26. 1 3 u 2 2 u
x
27. 28. 2x 23 5x 13 12 0
x 2 x 6 2
x 3 3
29. m 4 5m 2 36 0 30. 1y 2 15y 1 3
Solve the equation or inequality in Problems 31–35, and round
answers to three significant digits if necessary.
31. 2.15x 3.73(x 0.930) 6.11x
32. 1.52 0.770 2.04x 5.33
33. 9.71 3.62x 7 5.48
8
34. 2
3 4 5 t2 1 2
35. 6.09x 2 4.57x 8.86 0
Solve the equation in Problems 36–38 for the indicated variable in
terms of the other variables.
36. P M Mdt for M (mathematics of finance)
2
37. P EI RI for I (electrical engineering)
38. x 4y 5 for y
2y 1
39. Find the error in the following “solution” and then find the correct
solution.
4
x 2 4x 3 3
x 2 3x 2
4x 2 12x 8 3x 2 12x 9
x 2 1
x 1 or x 1