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. [latex]15(y-9)=-60[/latex]
2. [latex]21(y-5)=-42[/latex]
Solution
[latex]y=3[/latex]
3. [latex]-9(2n+1)=36[/latex]
4. [latex]-16(3n+4)=32[/latex]
Solution
[latex]n=-2[/latex]
5. [latex]8(22+11r)=0[/latex]
6. [latex]5(8+6p)=0[/latex]
Solution
[latex]p=-\frac{4}{3}[/latex]
7. [latex]-(w-12)=30[/latex]
8. [latex]-(t-19)=28[/latex]
Solution
[latex]t=-9[/latex]
9. [latex]9(6a+8)+9=81[/latex]
10. [latex]8(9b-4)-12=100[/latex]
Solution
[latex]b=2[/latex]
11. [latex]32+3(z+4)=41[/latex]
12. [latex]21+2(m-4)=25[/latex]
Solution
[latex]m=6[/latex]
13. [latex]51+5(4-q)=56[/latex]
14. [latex]-6+6(5-k)=15[/latex]
Solution
[latex]k=\frac{3}{2}[/latex]
15. [latex]2(9s-6)-62=16[/latex]
16. [latex]8(6t-5)-35=-27[/latex]
Solution
[latex]t=1[/latex]
17. [latex]3(10-2x)+54=0[/latex]
18. [latex]-2(11-7x)+54=4[/latex]
Solution
[latex]x=-2[/latex]
19. [latex]\frac{2}{3}(9c-3)=22[/latex]
20. [latex]\frac{3}{5}(10x-5)=27[/latex]
Solution
[latex]x=5[/latex]
21. [latex]\frac{1}{5}(15c+10)=c+7[/latex]
22. [latex]\frac{1}{4}(20d+12)=d+7[/latex]
Solution
[latex]d=1[/latex]
23. [latex]18-(9r+7)=-16[/latex]
24. [latex]15-(3r+8)=28[/latex]
Solution
[latex]r=-7[/latex]
25. [latex]5-(n-1)=19[/latex]
26. [latex]-3-(m-1)=13[/latex]
Solution
[latex]m=-15[/latex]
27. [latex]11-4(y-8)=43[/latex]
28. [latex]18-2(y-3)=32[/latex]
Solution
[latex]y=-4[/latex]
29. [latex]24-8(3v+6)=0[/latex]
30. [latex]35-5(2w+8)=-10[/latex]
Solution
[latex]w=\frac{1}{2}[/latex]
31. [latex]4(a-12)=3(a+5)[/latex]
32. [latex]-2(a-6)=4(a-3)[/latex]
Solution
[latex]a=4[/latex]
33. [latex]2(5-u)=-3(2u+6)[/latex]
34. [latex]5(8-r)=-2(2r-16)[/latex]
Solution
[latex]r=8[/latex]
35. [latex]3(4n-1)-2=8n+3[/latex]
36. [latex]9(2m-3)-8=4m+7[/latex]
Solution
[latex]m=3[/latex]
37. [latex]12+2(5-3y)=-9(y-1)-2[/latex]
38. [latex]-15+4(2-5y)=-7(y-4)+4[/latex]
Solution
[latex]y=-3[/latex]
39. [latex]8(x-4)-7x=14[/latex]
40. [latex]5(x-4)-4x=14[/latex]
Solution
[latex]x=34[/latex]
41. [latex]5+6(3s-5)=-3+2(8s-1)[/latex]
42. [latex]-12+8(x-5)=-4+3(5x-2)[/latex]
Solution
[latex]x=-6[/latex]
43. [latex]4(u-1)-8=6(3u-2)-7[/latex]
44. [latex]7(2n-5)=8(4n-1)-9[/latex]
Solution
[latex]n=-1[/latex]
45. [latex]4(p-4)-(p+7)=5(p-3)[/latex]
46. [latex]3(a-2)-(a+6)=4(a-1)[/latex]
Solution
[latex]a=-4[/latex]
47. [latex]-(9y+5)-(3y-7)=16-(4y-2)[/latex]
48. [latex]-(7m+4)-(2m-5)=14-(5m-3)[/latex]
Solution
[latex]m=-4[/latex]
49. [latex]4\left[5-8(4c-3)\right]=12(1-13c)-8[/latex]
50. [latex]5\left[9-2(6d-1)\right]=11(4-10d)-139[/latex]
Solution
[latex]d=-3[/latex]
51. [latex]3\left[-9+8(4h-3)\right]=2(5-12h)-19[/latex]
52. [latex]3\left[-14+2(15k-6)\right]=8(3-5k)-24[/latex]
Solution
[latex]k=\frac{3}{5}[/latex]
53. [latex]5\left[2(m+4)+8(m-7)\right]=2\left[3(5+m)-(21-3m)\right][/latex]
54. [latex]10\left[5(n+1)+4(n-1)\right]=11\left[7(5+n)-(25-3n)\right][/latex]
Solution
[latex]n=-5[/latex]
55. [latex]5(1.2u-4.8)=-12[/latex]
56. [latex]4(2.5v-0.6)=7.6[/latex]
Solution
[latex]v=1[/latex]
57. [latex]0.25(q-6)=0.1(q+18)[/latex]
58. [latex]0.2(p-6)=0.4(p+14)[/latex]
Solution
[latex]p=-34[/latex]
59. [latex]0.2(30n+50)=28[/latex]
60. [latex]0.5(16m+34)=-15[/latex]
Solution
[latex]m=-4[/latex]
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. [latex]23z+19=3(5z-9)+8z+46[/latex]
62. [latex]15y+32=2(10y-7)-5y+46[/latex]
Solution
identity; all real numbers
63. [latex]5(b-9)+4(3b+9)=6(4b-5)-7b+21[/latex]
64. [latex]9(a-4)+3(2a+5)=7(3a-4)-6a+7[/latex]
Solution
identity; all real numbers
65. [latex]18(5j-1)+29=47[/latex]
66. [latex]24(3d-4)+100=52[/latex]
Solution
conditional equation; [latex]d=\frac{2}{3}[/latex]
67. [latex]22(3m-4)=8(2m+9)[/latex]
68. [latex]30(2n-1)=5(10n+8)[/latex]
Solution
conditional equation; [latex]n=7[/latex]
69. [latex]7v+42=11(3v+8)-2(13v-1)[/latex]
70. [latex]18u-51=9(4u+5)-6(3u-10)[/latex]
Solution
contradiction; no solution
71. [latex]3(6q-9)+7(q+4)=5(6q+8)-5(q+1)[/latex]
72. [latex]5(p+4)+8(2p-1)=9(3p-5)-6(p-2)[/latex]
Solution
contradiction; no solution
73. [latex]12(6h-1)=8(8h+5)-4[/latex]
74. [latex]9(4k-7)=11(3k+1)+4[/latex]
Solution
conditional equation; [latex]k=26[/latex]
75. [latex]45(3y-2)=9(15y-6)[/latex]
76. [latex]60(2x-1)=15(8x+5)[/latex]
Solution
contradiction; no solution
77. [latex]16(6n+15)=48(2n+5)[/latex]
78. [latex]36(4m+5)=12(12m+15)[/latex]
Solution
identity; all real numbers
79. [latex]9(14d+9)+4d=13(10d+6)+3[/latex]
80. [latex]11(8c+5)-8c=2(40c+25)+5[/latex]
Solution
identity; all real numbers
Exercises: Everyday Math
Instructions: For questions 81-82, answer the given everyday math word problems.
81. Fencing. Micah has [latex]44[/latex] feet of fencing to make a dog run in his yard. He wants the length to be [latex]2.5[/latex] feet more than the width. Find the length, [latex]L[/latex], by solving the equation [latex]2L+2(L-2.5)=44[/latex].
89. Coins. Rhonda has [latex]$1.90[/latex] in nickels and dimes. The number of dimes is one less than twice the number of nickels. Find the number of nickels, [latex]n[/latex], by solving the equation [latex]0.05n+0.10(2n-1)=1.90[/latex].
Solution
[latex]8[/latex] 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
Answers will vary.
92. What is the first step you take when solving the equation [latex]3-7(y-4)=38[/latex]? Why is this your first step?
Solution
Answers will vary.
