1. Equations with Variables on Both Sides
ALGEBRA 1 LESSON 2-4
pages 98–101  Exercises
1. 9
2. 7
3. 3
4. 5
5. 7
6. 3
7. 3
8. –2
9. 7
10. –3
11. –3
21. a. Answers may vary.
Sample:
0 :  9 = 9
3 :  –9 = –9
–4 :  33 = 33
–6 :  45 = 45
b. identity
22. identity
23. no solution
24. identity
25. identity
26. no solution
27. no solution
28. no solution
12. 3
13. 2
14. 5
15. 4
16. 5
m = 22.95
+ 0.02m; 200 min
m = m;
11 months
19. 4b – 3 = 3b + 5; 8 ft
h = 250 +
70h; 15 h
2-4

2. Equations with Variables on Both Sides
ALGEBRA 1 LESSON 2-4
29. 0
30. identity
31. 10
32. no solution
33. no solution
34. –2
35. 0
36. identity
37. –
t = 12t;
375 teddy bears
b = 25b;
75 bags
40. x = –1, a = – , w = –4, y = 0
41. a = 3, b = 5, c = 7, d = 11
42. x = 5, w = 3, y = 2, a = 9
43. a = 3, b = 6, c = 5, d =
44. The student forgot a negative
sign on the left side of the
equation; –5.
45. The student subtracted y
from both sides instead of
adding y to both sides; 5.3.
46. DE = 10, DF = 7, EF = 6 1 4
47. No; an equation with
a solution of 0 has a
solution. An equation
with no solution is not
true for any value of
the variable.
48. a. no
b. 1 and 3; at 3,
4 – 3(x + 1) is
greater than 5(x – 3),
while at 1 the
opposite is true.
The values must be
the same for x
between 1 and 3.
c. for values of x
greater than 2 1 3 1 5 2 3
2-4

3. Equations with Variables on Both Sides
ALGEBRA 1 LESSON 2-4
49. Answers may vary.
Sample: 3x = 12x
50. Answers may vary.
Sample: 4x + 4 = 3x + 7
51. Answers may vary.
Sample: – = 2x + 7
52. Answers may vary.
Sample: 3x + 1 = 3(x + )
53. Answers may vary.
Sample: 14x – 12 = 7(2x + 3)
54. Answers may vary.
Sample: 7x – 2 = 5x
units
56. rectangle: 6 units, 2 units,
4 units, 4 units
57. D
58. G
59. C
60. H
61. C
62. I
63. A
64. 7
65. –4
67. –6
69. 1
in.
71. – , – , –
, 5.04, 5.043
, 8.1, 8.3
74. –100, –87, 93, 500
75. –1.24, 0.45, 1.23, 2.24
76. –9.8, 0.9, 8.6, 9.7 1 4 4 5 5 8 3 5 x 2 1 3 2 3
2-4