{"id":1367,"date":"2020-07-31T20:34:33","date_gmt":"2020-08-01T00:34:33","guid":{"rendered":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/5-review\/"},"modified":"2021-03-24T10:57:06","modified_gmt":"2021-03-24T14:57:06","slug":"5-review","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/5-review\/","title":{"raw":"5.8 Chapter Review","rendered":"5.8 Chapter Review"},"content":{"raw":"[latexpage]\n

Review Exercises<\/h1>\n

Verify a Solution of an Equation<\/h2>\n

In the following exercises, determine whether each number is a solution to the equation.<\/p>\n\n\n\n\n\n
1. \\(w-8=5,\\phantom{\\rule{0.2em}{0ex}}w=3\\)<\/td>\n2. \\(x+16=31,\\phantom{\\rule{0.2em}{0ex}}x=15\\)<\/td>\n<\/tr>\n
3. \\(4a=72,\\phantom{\\rule{0.2em}{0ex}}a=18\\)<\/td>\n4.\\(-9n=45,\\phantom{\\rule{0.2em}{0ex}}n=54\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Solve Equations using the Subtraction and Addition Properties of Equality<\/h2>\n

In the following exercises, solve each equation using the Subtraction Property of Equality.<\/p>\n\n

\n
\n\n\n\n\n
5. \\(y+2=-6\\)<\/td>\n6. \\(x+7=19\\)<\/td>\n<\/tr>\n
7. \\(n+3.6=5.1\\)<\/td>\n8. \\(a+\\frac{1}{3}=\\frac{5}{3}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
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\n

In the following exercises, solve each equation using the Addition Property of Equality.<\/p>\n\n\n\n\n\n
9. \\(x-9=-4\\)<\/td>\n10. \\(u-7=10\\)<\/td>\n<\/tr>\n
11. \\(p-4.8=14\\)<\/td>\n12. \\(c-\\frac{3}{11}=\\frac{9}{11}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n

In the following exercises, solve each equation.<\/p>\n\n\n\n\n\n
13. \\(y+16=-9\\)<\/td>\n14. \\(n-12=32\\)<\/td>\n<\/tr>\n
15. \\(d-3.9=8.2\\)<\/td>\n16. \\(f+\\frac{2}{3}=4\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Solve Equations That Require Simplification<\/h2>\n

In the following exercises, solve each equation.<\/p>\n\n\n\n\n\n
17. \\(7x+10-6x+3=5\\)<\/td>\n18. \\(y+8-15=-3\\)<\/td>\n<\/tr>\n
19. \\(8\\left(3p+5\\right)-23\\left(p-1\\right)=35\\)<\/td>\n20. \\(6\\left(n-1\\right)-5n=-14\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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\n

Translate to an Equation and Solve<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, translate each English sentence into an algebraic equation and then solve it.<\/p>\n\n\n\n\n
21. Four less than \\(n\\) is 13.<\/td>\n22. The sum of \\(-6\\) and \\(m\\) is 25.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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\n

Translate and Solve Applications<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, translate into an algebraic equation and solve.<\/p>\n\n\n\n\n\n
23. Tan weighs 146 pounds. Minh weighs 15 pounds more than Tan. How much does Minh weigh?<\/td>\n24. Rochelle\u2019s daughter is 11 years old. Her son is 3 years younger. How old is her son?<\/td>\n<\/tr>\n
25. Elissa earned \\$152.84 this week, which was \\$21.65 more than she earned last week. How much did she earn last week?<\/td>\n26. Peter paid \\$9.75 to go to the movies, which was \\$46.25 less than he paid to go to a concert. How much did he pay for the concert?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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Solve Equations Using the Division and Multiplication Properties of Equality<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, solve each equation using the division and multiplication properties of equality and check the solution.<\/p>\n\n\n\n\n\n\n\n\n\n
27. \\(13a=-65\\)<\/td>\n28. \\(8x=72\\)<\/td>\n<\/tr>\n
29. \\(-y=4\\)<\/td>\n30. \\(0.25p=5.25\\)<\/td>\n<\/tr>\n
31. \\(\\frac{y}{-10}=30\\)<\/td>\n32. \\(\\frac{n}{6}=18\\)<\/td>\n<\/tr>\n
33. \\(\\frac{5}{8}u=\\frac{15}{16}\\)<\/td>\n34. \\(36=\\frac{3}{4}x\\)<\/td>\n<\/tr>\n
35. \\(\\frac{c}{9}=36\\)<\/td>\n36. \\(-18m=-72\\)<\/td>\n<\/tr>\n
37. \\(\\frac{11}{12}=\\frac{2}{3}y\\)<\/td>\n38. \\(0.45x=6.75\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

Solve Equations That Require Simplification<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, solve each equation requiring simplification.<\/p>\n\n\n\n\n\n
39. \\(24x+8x-11x=-7-14\\)<\/td>\n40. \\(5r-3r+9r=35-2\\)<\/td>\n<\/tr>\n
41. \\(-9\\left(d-2\\right)-15=-24\\)<\/td>\n42. \\(\\frac{11}{12}n-\\frac{5}{6}n=9-5\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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Translate to an Equation and Solve<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, translate to an equation and then solve.<\/p>\n\n\n\n\n\n
43. The quotient of b<\/em> and and 9 is \\(-27\\).<\/td>\n44. 143 is the product of \\(-11\\) and y<\/em>.<\/td>\n<\/tr>\n
45. The difference of s<\/em> and one-twelfth is one fourth.<\/td>\n46. The sum of q<\/em> and one-fourth is one.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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Translate and Solve Applications<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, translate into an equation and solve.<\/p>\n\n\n\n\n
47. Janet gets paid \\$24 per hour. She heard that this is \\(\\frac{3}{4}\\) of what Adam is paid. How much is Adam paid per hour?<\/td>\n48. Ray paid \\$21 for 12 tickets at the county fair. What was the price of each ticket?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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Solve an Equation with Constants on Both Sides<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, solve the following equations with constants on both sides.<\/p>\n\n\n\n\n\n
49. \\(10w-5=65\\)<\/td>\n50. \\(8p+7=47\\)<\/td>\n<\/tr>\n
51. \\(32=-4-9n\\)<\/td>\n52. \\(3x+19=-47\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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Solve an Equation with Variables on Both Sides<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, solve the following equations with variables on both sides.<\/p>\n\n\n\n\n\n
53. \\(5a+21=2a\\)<\/td>\n54. \\(7y=6y-13\\)<\/td>\n<\/tr>\n
55. \\(4x-\\frac{3}{8}=3x\\)<\/td>\n56. \\(k=-6k-35\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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Solve an Equation with Variables and Constants on Both Sides<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, solve the following equations with variables and constants on both sides.<\/p>\n\n\n\n\n\n
57. \\(5n-20=-7n-80\\)<\/td>\n58. \\(12x-9=3x+45\\)<\/td>\n<\/tr>\n
59. \\(\\frac{5}{8}c-4=\\frac{3}{8}c+4\\)<\/td>\n60. \\(4u+16=-19-u\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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Solve Equations Using the General Strategy for Solving Linear Equations<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, solve each linear equation.<\/p>\n\n\n\n\n\n\n\n\n\n
61. \\(9\\left(2p-5\\right)=72\\)<\/td>\n62. \\(6\\left(x+6\\right)=24\\)<\/td>\n<\/tr>\n
63. \\(8+3\\left(n-9\\right)=17\\)<\/td>\n64. \\(\\text{-}\\left(s+4\\right)=18\\)<\/td>\n<\/tr>\n
65. \\(\\frac{1}{3}\\left(6m+21\\right)=m-7\\)<\/td>\n66. \\(23-3\\left(y-7\\right)=8\\)<\/td>\n<\/tr>\n
67. \\(0.25\\left(q-8\\right)=0.1\\left(q+7\\right)\\)<\/td>\n68. \\(4\\left(3.5y+0.25\\right)=365\\)<\/td>\n<\/tr>\n
69. \\(5+7\\left(2-5x\\right)=2\\left(9x+1\\right)\\) \\(-\\left(13x-57\\right)\\)<\/td>\n70. \\(8\\left(r-2\\right)=6\\left(r+10\\right)\\)<\/td>\n<\/tr>\n
71. \\(2\\left[-16+5\\left(8k-6\\right)\\right]\\) \\(=8\\left(3-4k\\right)-32\\)<\/td>\n72. \\(\\left(9n+5\\right)-\\left(3n-7\\right)\\) \\(=20-\\left(4n-2\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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Classify Equations<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution.<\/p>\n\n\n\n\n\n
73. \\(9u+32=15\\left(u-4\\right)\\) \\(-3\\left(2u+21\\right)\\)<\/td>\n74. \\(17y-3\\left(4-2y\\right)=11\\left(y-1\\right)\\) \\(+12y-1\\)<\/td>\n<\/tr>\n
75. \\(21\\left(c-1\\right)-19\\left(c+1\\right)\\) \\(=2\\left(c-20\\right)\\)<\/td>\n76. \\(-8\\left(7m+4\\right)=-6\\left(8m+9\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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Solve Equations with Fraction Coefficients<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, solve each equation with fraction coefficients.<\/p>\n\n\n\n\n\n\n
77. \\(\\frac{1}{3}x+\\frac{1}{5}x=8\\)<\/td>\n78. \\(\\frac{2}{5}n-\\frac{1}{10}=\\frac{7}{10}\\)<\/td>\n<\/tr>\n
79. \\(\\frac{1}{2}\\left(k-3\\right)=\\frac{1}{3}\\left(k+16\\right)\\)<\/td>\n80. \\(\\frac{3}{4}a-\\frac{1}{3}=\\frac{1}{2}a-\\frac{5}{6}\\)<\/td>\n<\/tr>\n
81. \\(\\frac{5y-1}{3}+4=\\frac{-8y+4}{6}\\)<\/td>\n82. \\(\\frac{3x-2}{5}=\\frac{3x+4}{8}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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Solve Equations with Decimal Coefficients<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, solve each equation with decimal coefficients.<\/p>\n\n\n\n\n
83. \\(0.36u+2.55=0.41u+6.8\\)<\/td>\n84. \\(0.8x-0.3=0.7x+0.2\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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Use the Distance, Rate, and Time Formula<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, solve.<\/p>\n\n\n\n\n\n
85. Mallory is taking the bus from Edmonton to North Battleford. The distance is 300 miles and the bus travels at a steady rate of 60 miles per hour. How long will the bus ride be?<\/td>\n86. Natalie drove for \\(7\\frac{1}{2}\\) hours at 60 miles per hour. How much distance did she travel?<\/td>\n<\/tr>\n
87. Link rode his bike at a steady rate of 15 miles per hour for \\(2\\frac{1}{2}\\) hours. How much distance did he travel?<\/td>\n88. Aaron\u2019s friend drove him from Williams Lake to Kamloops. The distance is 187 miles and the trip took 2.75 hours. How fast was Aaron\u2019s friend driving?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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Solve a Formula for a Specific Variable<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, solve.<\/p>\n\n\n\n\n\n\n\n
89. Use the formula. \\(d=rt\\) to solve for \\(r\\)\na) when when \\(d=451\\) and \\(t=5.5\\)\nb) in general<\/td>\n90. Use the formula. \\(d=rt\\) to solve for t<\/em>\na) when \\(d=510\\) and \\(r=60\\)\nb) in general<\/td>\n<\/tr>\n
91. Use the formula \\(A=\\frac{1}{2}bh\\) to solve for \\(h\\)\na) when \\(A=153\\) and \\(b=18\\)\nb) in general<\/td>\n92. Use the formula \\(A=\\frac{1}{2}bh\\) to solve for \\(b\\)\na) when \\(A=390\\) and \\(h=26\\)\nb) in general<\/td>\n<\/tr>\n
93. Solve the formula \\(4x+3y=6\\) for y<\/em>\na) when \\(x=-2\\)\nb) in general<\/td>\n94. Use the formula \\(I=Prt\\) to solve for the principal, P<\/em> for\na) \\(I=\\$2,501\\),\\(r=4.1\\%\\),\\(t=5\\phantom{\\rule{0.2em}{0ex}}\\text{years}\\)\nb) in general<\/td>\n<\/tr>\n
95. Solve the formula \\(V=LWH\\) for \\(H\\).<\/td>\n96. Solve \\(180=a+b+c\\) for \\(c\\).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Everyday Math<\/h2>\n\n\n\n
97. Describe how you have used two topics from this chapter in your life outside of your math class during the past month.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Review Exercises Answers<\/h1>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
1. no<\/td>\n3. yes<\/td>\n<\/tr>\n
5. \\(y=-8\\)<\/td>\n7. \\(n=1.5\\)<\/td>\n<\/tr>\n
9. \\(x=5\\)<\/td>\n11. \\(p=18.8\\)<\/td>\n<\/tr>\n
13. \\(y=-25\\)<\/td>\n15. \\(d=12.1\\)<\/td>\n<\/tr>\n
17. \\(x=-8\\)<\/td>\n19. \\(p=-28\\)<\/td>\n<\/tr>\n
21. \\(n-4=13;n=17\\)<\/td>\n23. 161 pounds<\/td>\n<\/tr>\n
25. \\$131.19<\/td>\n27. \\(a=-5\\)<\/td>\n<\/tr>\n
29. \\(y=-4\\)<\/td>\n31. \\(y=-300\\)<\/td>\n<\/tr>\n
33. \\(u=\\frac{3}{2}\\)<\/td>\n35. \\(c=324\\)<\/td>\n<\/tr>\n
37. \\(y=\\frac{11}{8}\\)<\/td>\n39. \\(x=-1\\)<\/td>\n<\/tr>\n
41. \\(d=3\\)<\/td>\n43. \\(\\frac{b}{9}=-27;b=-243\\)<\/td>\n<\/tr>\n
45. \\(s-\\frac{1}{12}=\\frac{1}{4};s=\\frac{1}{3}\\)<\/td>\n47. \\$32<\/td>\n<\/tr>\n
49. \\(w=7\\)<\/td>\n51. \\(n=-4\\)<\/td>\n<\/tr>\n
53. \\(a=-7\\)<\/td>\n55. \\(x=\\frac{3}{8}\\)<\/td>\n<\/tr>\n
57. \\(n=-5\\)<\/td>\n59. \\(c=32\\)<\/td>\n<\/tr>\n
61. \\(p=\\frac{13}{2}\\)<\/td>\n63. \\(n=12\\)<\/td>\n<\/tr>\n
65. \\(m=-14\\)<\/td>\n67. \\(q=18\\)<\/td>\n<\/tr>\n
69. \\(x=-1\\)<\/td>\n71. \\(k=\\frac{3}{4}\\)<\/td>\n<\/tr>\n
73. contradiction; no solution<\/td>\n75. identity; all real numbers<\/td>\n<\/tr>\n
77. \\(x=15\\)<\/td>\n79. \\(k=41\\)<\/td>\n<\/tr>\n
81. \\(y=-1\\)<\/td>\n83. \\(u=-85\\)<\/td>\n<\/tr>\n
85. 5 hours<\/td>\n87. 37.5 miles<\/td>\n<\/tr>\n
89. a)\\(r=82\\phantom{\\rule{0.2em}{0ex}}\\text{mph}\\); b)\\(r=\\frac{D}{t}\\)<\/td>\n91. a)\\(h=17\\)b)\\(h=\\frac{2A}{b}\\)<\/td>\n<\/tr>\n
93. a)\\(y=\\frac{14}{3}\\)b)\\(y=\\frac{6-4x}{3}\\)<\/td>\n95. \\(H=\\frac{V}{LW}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Practice Test<\/h1>\n
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Determine whether each number is a solution to the equation \\(3x+5=20\\).<\/p>\n\n\n\n\n
1.\na) 5\nb) \\(\\frac{23}{5}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nIn the following exercises, solve each equation.\n\n\n\n\n\n\n\n\n\n\n\n\n\n
2. \\(n-18=31\\)<\/td>\n3. \\(9c=144\\)<\/td>\n<\/tr>\n
4. \\(4y-8=16\\)<\/td>\n5. \\(-8x-15+9x-1=-21\\)<\/td>\n<\/tr>\n
6. \\(-15a=120\\)<\/td>\n7. \\(\\frac{2}{3}x=6\\)<\/td>\n<\/tr>\n
8. \\(x-3.8=8.2\\)<\/td>\n9. \\(10y=-5y-60\\)<\/td>\n<\/tr>\n
10. \\(8n-2=6n-12\\)<\/td>\n11. \\(9m-2-4m-m=42-8\\)<\/td>\n<\/tr>\n
12. \\(-5\\left(2x-1\\right)=45\\)<\/td>\n13. \\(\\text{-}\\left(d-9\\right)=23\\)<\/td>\n<\/tr>\n
14. \\(\\frac{1}{4}\\left(12m-28\\right)=6-2\\left(3m-1\\right)\\)<\/td>\n15. \\(2\\left(6x-5\\right)-8=-22\\)<\/td>\n<\/tr>\n
16.\\(8\\left(3a-5\\right)-7\\left(4a-3\\right)=20-3a\\)<\/td>\n17. \\(\\frac{1}{4}p-\\frac{1}{3}=\\frac{1}{2}\\)<\/td>\n<\/tr>\n
18. \\(0.1d+0.25\\left(d+8\\right)=4.1\\)<\/td>\n19. \\(14n-3\\left(4n+5\\right)=-9+2\\left(n-8\\right)\\)<\/td>\n<\/tr>\n
20. \\(9\\left(3u-2\\right)-4\\left[6-8\\left(u-1\\right)\\right]\\)\\(=3\\left(u-2\\right)\\)<\/td>\n21. Solve the formula \\(x-2y=5\\) for y<\/em>\na) when \\(x=-3\\)\nb) in general<\/td>\n<\/tr>\n
22. Samuel paid \\$25.82 for gas this week, which was \\$3.47 less than he paid last week. How much had he paid last week?<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n

Practice Test Answers<\/h1>\n\n\n\n\n\n\n\n\n\n\n\n\n\n
1. a) yes b) no<\/td>\n2. \\(n=49\\)<\/td>\n<\/tr>\n
3. \\(c=16\\)<\/td>\n4. \\(y=6\\)<\/td>\n<\/tr>\n
5. \\(x=-5\\)<\/td>\n6. \\(a=8\\)<\/td>\n<\/tr>\n
7. \\(x=9\\)<\/td>\n8. \\(x=12\\)<\/td>\n<\/tr>\n
9. \\(y=-4\\)<\/td>\n10. \\(n=-5\\)<\/td>\n<\/tr>\n
11. \\(m=9\\)<\/td>\n12. \\(x=-4\\)<\/td>\n<\/tr>\n
13. \\(d=-14\\)<\/td>\n14. \\(m=\\frac{5}{3}\\)<\/td>\n<\/tr>\n
15. \\(x=-\\frac{1}{3}\\)<\/td>\n16. \\(a=-39\\)<\/td>\n<\/tr>\n
17. \\(p=\\frac{10}{3}\\)<\/td>\n18. \\(d=6\\)<\/td>\n<\/tr>\n
19. contradiction; no solution<\/td>\n20. \\(u=\\frac{17}{14}\\)<\/td>\n<\/tr>\n
21. a) \\(y=4\\) b) \\(y=\\frac{5-x}{2}\\)<\/td>\n22. \\(\\$29.29\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\nAttributions<\/h1>\nThis chapter has been adapted from \"Review Exercises\" and \"Practice Test\" in Chapter 2 of Elementary Algebra<\/em> (OpenStax)<\/a> by Lynn Marecek and MaryAnne Anthony-Smith, which is under a CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.","rendered":"

Review Exercises<\/h1>\n

Verify a Solution of an Equation<\/h2>\n

In the following exercises, determine whether each number is a solution to the equation.<\/p>\n\n\n\n\n
1. \"w-8=5,\phantom{\rule{0.2em}{0ex}}w=3\"<\/td>\n2. \"x+16=31,\phantom{\rule{0.2em}{0ex}}x=15\"<\/td>\n<\/tr>\n
3. \"4a=72,\phantom{\rule{0.2em}{0ex}}a=18\"<\/td>\n4.\"-9n=45,\phantom{\rule{0.2em}{0ex}}n=54\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Solve Equations using the Subtraction and Addition Properties of Equality<\/h2>\n

In the following exercises, solve each equation using the Subtraction Property of Equality.<\/p>\n

\n
\n\n\n\n\n
5. \"y+2=-6\"<\/td>\n6. \"x+7=19\"<\/td>\n<\/tr>\n
7. \"n+3.6=5.1\"<\/td>\n8. \"a+\frac{1}{3}=\frac{5}{3}\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
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In the following exercises, solve each equation using the Addition Property of Equality.<\/p>\n\n\n\n\n
9. \"x-9=-4\"<\/td>\n10. \"u-7=10\"<\/td>\n<\/tr>\n
11. \"p-4.8=14\"<\/td>\n12. \"c-\frac{3}{11}=\frac{9}{11}\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n

In the following exercises, solve each equation.<\/p>\n\n\n\n\n
13. \"y+16=-9\"<\/td>\n14. \"n-12=32\"<\/td>\n<\/tr>\n
15. \"d-3.9=8.2\"<\/td>\n16. \"f+\frac{2}{3}=4\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Solve Equations That Require Simplification<\/h2>\n

In the following exercises, solve each equation.<\/p>\n\n\n\n\n
17. \"7x+10-6x+3=5\"<\/td>\n18. \"y+8-15=-3\"<\/td>\n<\/tr>\n
19. \"8\left(3p+5\right)-23\left(p-1\right)=35\"<\/td>\n20. \"6\left(n-1\right)-5n=-14\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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Translate to an Equation and Solve<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, translate each English sentence into an algebraic equation and then solve it.<\/p>\n\n\n\n
21. Four less than \"n\" is 13.<\/td>\n22. The sum of \"-6\" and \"m\" is 25.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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Translate and Solve Applications<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, translate into an algebraic equation and solve.<\/p>\n\n\n\n\n
23. Tan weighs 146 pounds. Minh weighs 15 pounds more than Tan. How much does Minh weigh?<\/td>\n24. Rochelle\u2019s daughter is 11 years old. Her son is 3 years younger. How old is her son?<\/td>\n<\/tr>\n
25. Elissa earned $152.84 this week, which was $21.65 more than she earned last week. How much did she earn last week?<\/td>\n26. Peter paid $9.75 to go to the movies, which was $46.25 less than he paid to go to a concert. How much did he pay for the concert?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

Solve Equations Using the Division and Multiplication Properties of Equality<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, solve each equation using the division and multiplication properties of equality and check the solution.<\/p>\n\n\n\n\n\n\n\n\n
27. \"13a=-65\"<\/td>\n28. \"8x=72\"<\/td>\n<\/tr>\n
29. \"-y=4\"<\/td>\n30. \"0.25p=5.25\"<\/td>\n<\/tr>\n
31. \"\frac{y}{-10}=30\"<\/td>\n32. \"\frac{n}{6}=18\"<\/td>\n<\/tr>\n
33. \"\frac{5}{8}u=\frac{15}{16}\"<\/td>\n34. \"36=\frac{3}{4}x\"<\/td>\n<\/tr>\n
35. \"\frac{c}{9}=36\"<\/td>\n36. \"-18m=-72\"<\/td>\n<\/tr>\n
37. \"\frac{11}{12}=\frac{2}{3}y\"<\/td>\n38. \"0.45x=6.75\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

Solve Equations That Require Simplification<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, solve each equation requiring simplification.<\/p>\n\n\n\n\n
39. \"24x+8x-11x=-7-14\"<\/td>\n40. \"5r-3r+9r=35-2\"<\/td>\n<\/tr>\n
41. \"-9\left(d-2\right)-15=-24\"<\/td>\n42. \"\frac{11}{12}n-\frac{5}{6}n=9-5\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

Translate to an Equation and Solve<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, translate to an equation and then solve.<\/p>\n\n\n\n\n
43. The quotient of b<\/em> and and 9 is \"-27\".<\/td>\n44. 143 is the product of \"-11\" and y<\/em>.<\/td>\n<\/tr>\n
45. The difference of s<\/em> and one-twelfth is one fourth.<\/td>\n46. The sum of q<\/em> and one-fourth is one.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

Translate and Solve Applications<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, translate into an equation and solve.<\/p>\n\n\n\n
47. Janet gets paid $24 per hour. She heard that this is \"\frac{3}{4}\" of what Adam is paid. How much is Adam paid per hour?<\/td>\n48. Ray paid $21 for 12 tickets at the county fair. What was the price of each ticket?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

Solve an Equation with Constants on Both Sides<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, solve the following equations with constants on both sides.<\/p>\n\n\n\n\n
49. \"10w-5=65\"<\/td>\n50. \"8p+7=47\"<\/td>\n<\/tr>\n
51. \"32=-4-9n\"<\/td>\n52. \"3x+19=-47\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

Solve an Equation with Variables on Both Sides<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, solve the following equations with variables on both sides.<\/p>\n\n\n\n\n
53. \"5a+21=2a\"<\/td>\n54. \"7y=6y-13\"<\/td>\n<\/tr>\n
55. \"4x-\frac{3}{8}=3x\"<\/td>\n56. \"k=-6k-35\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

Solve an Equation with Variables and Constants on Both Sides<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, solve the following equations with variables and constants on both sides.<\/p>\n\n\n\n\n
57. \"5n-20=-7n-80\"<\/td>\n58. \"12x-9=3x+45\"<\/td>\n<\/tr>\n
59. \"\frac{5}{8}c-4=\frac{3}{8}c+4\"<\/td>\n60. \"4u+16=-19-u\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

Solve Equations Using the General Strategy for Solving Linear Equations<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, solve each linear equation.<\/p>\n\n\n\n\n\n\n\n\n
61. \"9\left(2p-5\right)=72\"<\/td>\n62. \"6\left(x+6\right)=24\"<\/td>\n<\/tr>\n
63. \"8+3\left(n-9\right)=17\"<\/td>\n64. \"\text{-}\left(s+4\right)=18\"<\/td>\n<\/tr>\n
65. \"\frac{1}{3}\left(6m+21\right)=m-7\"<\/td>\n66. \"23-3\left(y-7\right)=8\"<\/td>\n<\/tr>\n
67. \"0.25\left(q-8\right)=0.1\left(q+7\right)\"<\/td>\n68. \"4\left(3.5y+0.25\right)=365\"<\/td>\n<\/tr>\n
69. \"5+7\left(2-5x\right)=2\left(9x+1\right)\" \"-\left(13x-57\right)\"<\/td>\n70. \"8\left(r-2\right)=6\left(r+10\right)\"<\/td>\n<\/tr>\n
71. \"2\left[-16+5\left(8k-6\right)\right]\" \"=8\left(3-4k\right)-32\"<\/td>\n72. \"\left(9n+5\right)-\left(3n-7\right)\" \"=20-\left(4n-2\right)\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

Classify Equations<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution.<\/p>\n\n\n\n\n
73. \"9u+32=15\left(u-4\right)\" \"-3\left(2u+21\right)\"<\/td>\n74. \"17y-3\left(4-2y\right)=11\left(y-1\right)\" \"+12y-1\"<\/td>\n<\/tr>\n
75. \"21\left(c-1\right)-19\left(c+1\right)\" \"=2\left(c-20\right)\"<\/td>\n76. \"-8\left(7m+4\right)=-6\left(8m+9\right)\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

Solve Equations with Fraction Coefficients<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, solve each equation with fraction coefficients.<\/p>\n\n\n\n\n\n
77. \"\frac{1}{3}x+\frac{1}{5}x=8\"<\/td>\n78. \"\frac{2}{5}n-\frac{1}{10}=\frac{7}{10}\"<\/td>\n<\/tr>\n
79. \"\frac{1}{2}\left(k-3\right)=\frac{1}{3}\left(k+16\right)\"<\/td>\n80. \"\frac{3}{4}a-\frac{1}{3}=\frac{1}{2}a-\frac{5}{6}\"<\/td>\n<\/tr>\n
81. \"\frac{5y-1}{3}+4=\frac{-8y+4}{6}\"<\/td>\n82. \"\frac{3x-2}{5}=\frac{3x+4}{8}\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

Solve Equations with Decimal Coefficients<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, solve each equation with decimal coefficients.<\/p>\n\n\n\n
83. \"0.36u+2.55=0.41u+6.8\"<\/td>\n84. \"0.8x-0.3=0.7x+0.2\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

Use the Distance, Rate, and Time Formula<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, solve.<\/p>\n\n\n\n\n
85. Mallory is taking the bus from Edmonton to North Battleford. The distance is 300 miles and the bus travels at a steady rate of 60 miles per hour. How long will the bus ride be?<\/td>\n86. Natalie drove for \"7\frac{1}{2}\" hours at 60 miles per hour. How much distance did she travel?<\/td>\n<\/tr>\n
87. Link rode his bike at a steady rate of 15 miles per hour for \"2\frac{1}{2}\" hours. How much distance did he travel?<\/td>\n88. Aaron\u2019s friend drove him from Williams Lake to Kamloops. The distance is 187 miles and the trip took 2.75 hours. How fast was Aaron\u2019s friend driving?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

Solve a Formula for a Specific Variable<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, solve.<\/p>\n\n\n\n\n\n\n
89. Use the formula. \"d=rt\" to solve for \"r\"
\na) when when \"d=451\" and \"t=5.5\"
\nb) in general<\/td>\n		90. Use the formula. \"d=rt\" to solve for t<\/em>
\na) when \"d=510\" and \"r=60\"
\nb) in general<\/td>\n<\/tr>\n
91. Use the formula \"A=\frac{1}{2}bh\" to solve for \"h\"
\na) when \"A=153\" and \"b=18\"
\nb) in general<\/td>\n		92. Use the formula \"A=\frac{1}{2}bh\" to solve for \"b\"
\na) when \"A=390\" and \"h=26\"
\nb) in general<\/td>\n<\/tr>\n
93. Solve the formula \"4x+3y=6\" for y<\/em>
\na) when \"x=-2\"
\nb) in general<\/td>\n		94. Use the formula \"I=Prt\" to solve for the principal, P<\/em> for
\na) \"I=\$2,501\",\"r=4.1\%\",\"t=5\phantom{\rule{0.2em}{0ex}}\text{years}\"
\nb) in general<\/td>\n<\/tr>\n
95. Solve the formula \"V=LWH\" for \"H\".<\/td>\n96. Solve \"180=a+b+c\" for \"c\".<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Everyday Math<\/h2>\n\n\n\n
97. Describe how you have used two topics from this chapter in your life outside of your math class during the past month.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Review Exercises Answers<\/h1>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
1. no<\/td>\n3. yes<\/td>\n<\/tr>\n
5. \"y=-8\"<\/td>\n7. \"n=1.5\"<\/td>\n<\/tr>\n
9. \"x=5\"<\/td>\n11. \"p=18.8\"<\/td>\n<\/tr>\n
13. \"y=-25\"<\/td>\n15. \"d=12.1\"<\/td>\n<\/tr>\n
17. \"x=-8\"<\/td>\n19. \"p=-28\"<\/td>\n<\/tr>\n
21. \"n-4=13;n=17\"<\/td>\n23. 161 pounds<\/td>\n<\/tr>\n
25. $131.19<\/td>\n27. \"a=-5\"<\/td>\n<\/tr>\n
29. \"y=-4\"<\/td>\n31. \"y=-300\"<\/td>\n<\/tr>\n
33. \"u=\frac{3}{2}\"<\/td>\n35. \"c=324\"<\/td>\n<\/tr>\n
37. \"y=\frac{11}{8}\"<\/td>\n39. \"x=-1\"<\/td>\n<\/tr>\n
41. \"d=3\"<\/td>\n43. \"\frac{b}{9}=-27;b=-243\"<\/td>\n<\/tr>\n
45. \"s-\frac{1}{12}=\frac{1}{4};s=\frac{1}{3}\"<\/td>\n47. $32<\/td>\n<\/tr>\n
49. \"w=7\"<\/td>\n51. \"n=-4\"<\/td>\n<\/tr>\n
53. \"a=-7\"<\/td>\n55. \"x=\frac{3}{8}\"<\/td>\n<\/tr>\n
57. \"n=-5\"<\/td>\n59. \"c=32\"<\/td>\n<\/tr>\n
61. \"p=\frac{13}{2}\"<\/td>\n63. \"n=12\"<\/td>\n<\/tr>\n
65. \"m=-14\"<\/td>\n67. \"q=18\"<\/td>\n<\/tr>\n
69. \"x=-1\"<\/td>\n71. \"k=\frac{3}{4}\"<\/td>\n<\/tr>\n
73. contradiction; no solution<\/td>\n75. identity; all real numbers<\/td>\n<\/tr>\n
77. \"x=15\"<\/td>\n79. \"k=41\"<\/td>\n<\/tr>\n
81. \"y=-1\"<\/td>\n83. \"u=-85\"<\/td>\n<\/tr>\n
85. 5 hours<\/td>\n87. 37.5 miles<\/td>\n<\/tr>\n
89. a)\"r=82\phantom{\rule{0.2em}{0ex}}\text{mph}\"; b)\"r=\frac{D}{t}\"<\/td>\n91. a)\"h=17\"b)\"h=\frac{2A}{b}\"<\/td>\n<\/tr>\n
93. a)\"y=\frac{14}{3}\"b)\"y=\frac{6-4x}{3}\"<\/td>\n95. \"H=\frac{V}{LW}\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Practice Test<\/h1>\n
\n
\n

Determine whether each number is a solution to the equation \"3x+5=20\".<\/p>\n\n\n\n
1.
\na) 5
\nb) \"\frac{23}{5}\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

In the following exercises, solve each equation.<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n
2. \"n-18=31\"<\/td>\n3. \"9c=144\"<\/td>\n<\/tr>\n
4. \"4y-8=16\"<\/td>\n5. \"-8x-15+9x-1=-21\"<\/td>\n<\/tr>\n
6. \"-15a=120\"<\/td>\n7. \"\frac{2}{3}x=6\"<\/td>\n<\/tr>\n
8. \"x-3.8=8.2\"<\/td>\n9. \"10y=-5y-60\"<\/td>\n<\/tr>\n
10. \"8n-2=6n-12\"<\/td>\n11. \"9m-2-4m-m=42-8\"<\/td>\n<\/tr>\n
12. \"-5\left(2x-1\right)=45\"<\/td>\n13. \"\text{-}\left(d-9\right)=23\"<\/td>\n<\/tr>\n
14. \"\frac{1}{4}\left(12m-28\right)=6-2\left(3m-1\right)\"<\/td>\n15. \"2\left(6x-5\right)-8=-22\"<\/td>\n<\/tr>\n
16.\"8\left(3a-5\right)-7\left(4a-3\right)=20-3a\"<\/td>\n17. \"\frac{1}{4}p-\frac{1}{3}=\frac{1}{2}\"<\/td>\n<\/tr>\n
18. \"0.1d+0.25\left(d+8\right)=4.1\"<\/td>\n19. \"14n-3\left(4n+5\right)=-9+2\left(n-8\right)\"<\/td>\n<\/tr>\n
20. \"9\left(3u-2\right)-4\left[6-8\left(u-1\right)\right]\"\"=3\left(u-2\right)\"<\/td>\n21. Solve the formula \"x-2y=5\" for y<\/em>
\na) when \"x=-3\"
\nb) in general<\/td>\n<\/tr>\n
22. Samuel paid $25.82 for gas this week, which was $3.47 less than he paid last week. How much had he paid last week?<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n

Practice Test Answers<\/h1>\n\n\n\n\n\n\n\n\n\n\n\n\n\n
1. a) yes b) no<\/td>\n2. \"n=49\"<\/td>\n<\/tr>\n
3. \"c=16\"<\/td>\n4. \"y=6\"<\/td>\n<\/tr>\n
5. \"x=-5\"<\/td>\n6. \"a=8\"<\/td>\n<\/tr>\n
7. \"x=9\"<\/td>\n8. \"x=12\"<\/td>\n<\/tr>\n
9. \"y=-4\"<\/td>\n10. \"n=-5\"<\/td>\n<\/tr>\n
11. \"m=9\"<\/td>\n12. \"x=-4\"<\/td>\n<\/tr>\n
13. \"d=-14\"<\/td>\n14. \"m=\frac{5}{3}\"<\/td>\n<\/tr>\n
15. \"x=-\frac{1}{3}\"<\/td>\n16. \"a=-39\"<\/td>\n<\/tr>\n
17. \"p=\frac{10}{3}\"<\/td>\n18. \"d=6\"<\/td>\n<\/tr>\n
19. contradiction; no solution<\/td>\n20. \"u=\frac{17}{14}\"<\/td>\n<\/tr>\n
21. a) \"y=4\" b) \"y=\frac{5-x}{2}\"<\/td>\n22. \"\$29.29\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\nAttributions<\/h1>\n

This chapter has been adapted from “Review Exercises” and “Practice Test” in Chapter 2 of Elementary Algebra<\/em> (OpenStax)<\/a> by Lynn Marecek and MaryAnne Anthony-Smith, which is under a CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.<\/p>\n","protected":false},"author":90,"menu_order":9,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1367","chapter","type-chapter","status-publish","hentry"],"part":767,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1367","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1367\/revisions"}],"predecessor-version":[{"id":1368,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1367\/revisions\/1368"}],"part":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/parts\/767"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1367\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/media?parent=1367"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1367"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/contributor?post=1367"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/license?post=1367"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}