# Exercises: Use a General Strategy to Solve Linear Equations (3.4)

## Exercises: Solve Equations Using the General Strategy for Solving Linear Equations

Instructions: For questions 1-60, solve each linear equation.

1. $15(y-9)=-60$

2. $21(y-5)=-42$

Solution

$y=3$

3. $-9(2n+1)=36$

4. $-16(3n+4)=32$

Solution

$n=-2$

5. $8(22+11r)=0$

6. $5(8+6p)=0$

Solution

$p=-\frac{4}{3}$

7. $-(w-12)=30$

8. $-(t-19)=28$

Solution

$t=-9$

9. $9(6a+8)+9=81$

10. $8(9b-4)-12=100$

Solution

$b=2$

11. $32+3(z+4)=41$

12. $21+2(m-4)=25$

Solution

$m=6$

13. $51+5(4-q)=56$

14. $-6+6(5-k)=15$

Solution

$k=\frac{3}{2}$

15. $2(9s-6)-62=16$

16. $8(6t-5)-35=-27$

Solution

$t=1$

17. $3(10-2x)+54=0$

18. $-2(11-7x)+54=4$

Solution

$x=-2$

19. $\frac{2}{3}(9c-3)=22$

20. $\frac{3}{5}(10x-5)=27$

Solution

$x=5$

21. $\frac{1}{5}(15c+10)=c+7$

22. $\frac{1}{4}(20d+12)=d+7$

Solution

$d=1$

23. $18-(9r+7)=-16$

24. $15-(3r+8)=28$

Solution

$r=-7$

25. $5-(n-1)=19$

26. $-3-(m-1)=13$

Solution

$m=-15$

27. $11-4(y-8)=43$

28. $18-2(y-3)=32$

Solution

$y=-4$

29. $24-8(3v+6)=0$

30. $35-5(2w+8)=-10$

Solution

$w=\frac{1}{2}$

31. $4(a-12)=3(a+5)$

32. $-2(a-6)=4(a-3)$

Solution

$a=4$

33. $2(5-u)=-3(2u+6)$

34. $5(8-r)=-2(2r-16)$

Solution

$r=8$

35. $3(4n-1)-2=8n+3$

36. $9(2m-3)-8=4m+7$

Solution

$m=3$

37. $12+2(5-3y)=-9(y-1)-2$

38. $-15+4(2-5y)=-7(y-4)+4$

Solution

$y=-3$

39. $8(x-4)-7x=14$

40. $5(x-4)-4x=14$

Solution

$x=34$

41. $5+6(3s-5)=-3+2(8s-1)$

42. $-12+8(x-5)=-4+3(5x-2)$

Solution

$x=-6$

43. $4(u-1)-8=6(3u-2)-7$

44. $7(2n-5)=8(4n-1)-9$

Solution

$n=-1$

45. $4(p-4)-(p+7)=5(p-3)$

46. $3(a-2)-(a+6)=4(a-1)$

Solution

$a=-4$

47. $-(9y+5)-(3y-7)=16-(4y-2)$

48. $-(7m+4)-(2m-5)=14-(5m-3)$

Solution

$m=-4$

49. $4\left[5-8(4c-3)\right]=12(1-13c)-8$

50. $5\left[9-2(6d-1)\right]=11(4-10d)-139$

Solution

$d=-3$

51. $3\left[-9+8(4h-3)\right]=2(5-12h)-19$

52. $3\left[-14+2(15k-6)\right]=8(3-5k)-24$

Solution

$k=\frac{3}{5}$

53. $5\left[2(m+4)+8(m-7)\right]=2\left[3(5+m)-(21-3m)\right]$

54. $10\left[5(n+1)+4(n-1)\right]=11\left[7(5+n)-(25-3n)\right]$

Solution

$n=-5$

55. $5(1.2u-4.8)=-12$

56. $4(2.5v-0.6)=7.6$

Solution

$v=1$

57. $0.25(q-6)=0.1(q+18)$

58. $0.2(p-6)=0.4(p+14)$

Solution

$p=-34$

59. $0.2(30n+50)=28$

60. $0.5(16m+34)=-15$

Solution

$m=-4$

## Exercises: Classify Equations

Instructions: For questions 61-80, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution.

61. $23z+19=3(5z-9)+8z+46$

62. $15y+32=2(10y-7)-5y+46$

Solution

identity; all real numbers

63. $5(b-9)+4(3b+9)=6(4b-5)-7b+21$

64. $9(a-4)+3(2a+5)=7(3a-4)-6a+7$

Solution

identity; all real numbers

65. $18(5j-1)+29=47$

66. $24(3d-4)+100=52$

Solution

conditional equation; $d=\frac{2}{3}$

67. $22(3m-4)=8(2m+9)$

68. $30(2n-1)=5(10n+8)$

Solution

conditional equation; $n=7$

69. $7v+42=11(3v+8)-2(13v-1)$

70. $18u-51=9(4u+5)-6(3u-10)$

Solution

71. $3(6q-9)+7(q+4)=5(6q+8)-5(q+1)$

72. $5(p+4)+8(2p-1)=9(3p-5)-6(p-2)$

Solution

73. $12(6h-1)=8(8h+5)-4$

74. $9(4k-7)=11(3k+1)+4$

Solution

conditional equation; $k=26$

75. $45(3y-2)=9(15y-6)$

76. $60(2x-1)=15(8x+5)$

Solution

77. $16(6n+15)=48(2n+5)$

78. $36(4m+5)=12(12m+15)$

Solution

identity; all real numbers

79. $9(14d+9)+4d=13(10d+6)+3$

80. $11(8c+5)-8c=2(40c+25)+5$

Solution

identity; all real numbers

## Exercises: Everyday Math

Instructions: For questions 81-82, answer the given everyday math word problems.

81. Fencing. Micah has $44$ feet of fencing to make a dog run in his yard. He wants the length to be $2.5$ feet more than the width. Find the length, $L$, by solving the equation $2L+2(L-2.5)=44$.

89. Coins. Rhonda has $1.90$ in nickels and dimes. The number of dimes is one less than twice the number of nickels. Find the number of nickels, $n$, by solving the equation $0.05n+0.10(2n-1)=1.90$.

Solution

$8$ nickels

## Exercises: Writing Exercises

Instructions: For questions 90-93, answer the given writing exercises.

90. Using your own words, list the steps in the general strategy for solving linear equations.

91. Explain why you should simplify both sides of an equation as much as possible before collecting the variable terms to one side and the constant terms to the other side.

Solution

92. What is the first step you take when solving the equation $3-7(y-4)=38$? Why is this your first step?

93. Solve the equation $\frac{1}{4}(8x+20)=3x-4$ explaining all the steps of your solution as in the examples in this section.
Solution