Chapter 2 Review Exercises
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Chapter 2 Review Exercises
Solve Equations using the Subtraction and Addition Properties of Equality
Verify a Solution of an Equation
In the following exercises, determine whether each number is a solution to the equation.
Exercise 1
10x−1=5x;x=15
Exercise 2
w+2=58;w=38
- Answer
-
no
Exercise 3
−12n+5=8n;n=−54
Exercise 4
6a−3=−7a,a=313
- Answer
-
yes
Solve Equations using the Subtraction and Addition Properties of Equality
In the following exercises, solve each equation using the Subtraction Property of Equality.
Exercise 5
x+7=19
Exercise 6
y+2=−6
- Answer
-
y=−8
Exercise 7
a+13=53
Exercise 8
n+3.6=5.1
- Answer
-
n=1.5
In the following exercises, solve each equation using the Addition Property of Equality.
Exercise 9
u−7=10
Exercise 10
x−9=−4
- Answer
-
x=5
Exercise 11
c−311=911
Exercise 12
p−4.8=14
- Answer
-
p=18.8
In the following exercises, solve each equation.
Exercise 13
n−12=32
Exercise 14
y+16=−9
- Answer
-
y=−25
Exercise 15
f+23=4
Exercise 16
d−3.9=8.2
- Answer
-
d=12.1
Solve Equations That Require Simplification
In the following exercises, solve each equation.
Exercise 17
y+8−15=−3
Exercise 18
7x+10−6x+3=5
- Answer
-
x=−8
Exercise 19
6(n−1)−5n=−14
Exercise 20
8(3p+5)−23(p−1)=35
- Answer
-
p=−28
Translate to an Equation and Solve
In the following exercises, translate each English sentence into an algebraic equation and then solve it.
Exercise 21
The sum of −6 and m is 25
Exercise 22
Four less than n is 13
- Answer
-
n−4=13;n=17
Translate and Solve Applications
In the following exercises, translate into an algebraic equation and solve.
Exercise 23
Rochelle’s daughter is 11 years old. Her son is 3 years younger. How old is her son?
Exercise 24
Tan weighs 146 pounds. Minh weighs 15 pounds more than Tan. How much does Minh weigh?
- Answer
-
161 pounds
Exercise 25
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?
Exercise 26
Elissa earned $152.84 this week, which was $2..65 more than she earned last week. How much did she earn last week?
- Answer
-
$131.19
Solve Equations using the Division and Multiplication Properties of Equality
Solve Equations Using the Division and Multiplication Properties of Equality
In the following exercises, solve each equation using the division and multiplication properties of equality and check the solution.
Exercise 27
8x=72
Exercise 28
13a=−65
- Answer
-
a=−5
Exercise 29
0.25p=5.25
Exercise 30
−y=4
- Answer
-
y=−4
Exercise 31
n6=18
Exercise 32
y−10=30
- Answer
-
y=−300
Exercise 33
36=34x
Exercise 34
58u=1516
- Answer
-
u=32
Exercise 35
−18m=−72
Exercise 36
c9=36
- Answer
-
c=324
Exercise 37
0.45x=6.75
Exercise 38
1112=23y
- Answer
-
y=118
Solve Equations That Require Simplification
In the following exercises, solve each equation requiring simplification.
Exercise 39
5r−3r+9r=35−2
Exercise 40
24x+8x−11x=−7−14
- Answer
-
x=−1
Exercise 41
1112n−56n=9−5
Exercise 42
−9(d−2)−15=−24
- Answer
-
d=3
Translate to an Equation and Solve
In the following exercises, translate to an equation and then solve.
Exercise 43
143 is the product of −11 and y
Exercise 44
The quotient of b and and 9 is −27
- Answer
-
b9=−27;b=−243
Exercise 45
The sum of q and one-fourth is one.
Exercise 46
The difference of s and one-twelfth is one fourth.
- Answer
-
s−112=14;s=13
Translate and Solve Applications
In the following exercises, translate into an equation and solve.
Exercise 47
Ray paid $21 for 12 tickets at the county fair. What was the price of each ticket?
Exercise 48
Janet gets paid $24 per hour. She heard that this is 34 of what Adam is paid. How much is Adam paid per hour?
- Answer
-
$32
Solve Equations with Variables and Constants on Both Sides
Solve an Equation with Constants on Both Sides
In the following exercises, solve the following equations with constants on both sides.
Exercise 49
8p+7=47
Exercise 50
10w−5=65
- Answer
-
w=7
Exercise 51
3x+19=−47
Exercise 52
32=−4−9n
- Answer
-
n=−4
Solve an Equation with Variables on Both Sides
In the following exercises, solve the following equations with variables on both sides.
Exercise 53
7y=6y−13
Exercise 54
5a+21=2a
- Answer
-
a=−7
Exercise 55
k=−6k−35
Exercise 56
4x−38=3x
- Answer
-
x=38
Solve an Equation with Variables and Constants on Both Sides
In the following exercises, solve the following equations with variables and constants on both sides.
Exercise 57
12x−9=3x+45
Exercise 58
5n−20=−7n−80
- Answer
-
n=−5
Exercise 59
4u+16=−19−u
Exercise 60
58c−4=38c+4
- Answer
-
c=32
Use a General Strategy for Solving Linear Equations
Solve Equations Using the General Strategy for Solving Linear Equations
In the following exercises, solve each linear equation.
Exercise 61
6(x+6)=24
Exercise 62
9(2p−5)=72
- Answer
-
p=132
Exercise 63
−(s+4)=18
Exercise 64
8+3(n−9)=17
- Answer
-
n=12
Exercise 65
23−3(y−7)=8
Exercise 66
13(6m+21)=m−7
- Answer
-
m=−14
Exercise 67
4(3.5y+0.25)=365
Exercise 68
0.25(q−8)=0.1(q+7)
- Answer
-
q=18
Exercise 69
8(r−2)=6(r+10)
Exercise 70
5+7(2−5x)=2(9x+1)−(13x−57)
- Answer
-
x=−1
Exercise 71
(9n+5)−(3n−7)=20−(4n−2)
Exercise 72
2[−16+5(8k−6)]=8(3−4k)−32
- Answer
-
k=34
Classify Equations
In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution.
Exercise 73
17y−3(4−2y)=11(y−1)+12y−1
Exercise 74
9u+32=15(u−4)−3(2u+21)
- Answer
-
contradiction; no solution
Exercise 75
−8(7m+4)=−6(8m+9)
Exercise 76
21(c−1)−19(c+1)=2(c−20)
- Answer
-
identity; all real numbers
Solve Equations with Fractions and Decimals
Solve Equations with Fraction Coefficients
In the following exercises, solve each equation with fraction coefficients.
Exercise 77
25n−110=710
Exercise 78
13x+15x=8
- Answer
-
x=15
Exercise 79
34a−13=12a−56
Exercise 80
12(k−3)=13(k+16)
- Answer
-
k=41
Exercise 81
3x−25=3x+48
Exercise 82
5y−13+4=−8y+46
- Answer
-
y=−1
Solve Equations with Decimal Coefficients
In the following exercises, solve each equation with decimal coefficients.
Exercise 83
0.8x−0.3=0.7x+0.2
Exercise 84
0.36u+2.55=0.41u+6.8
- Answer
-
u=−85
Exercise 85
0.6p−1.9=0.78p+1.7
Exercise 86
0.6p−1.9=0.78p+1.7
- Answer
-
d=−20
Solve a Formula for a Specific Variable
Use the Distance, Rate, and Time Formula
In the following exercises, solve.
Exercise 87
Natalie drove for 712 hours at 60 miles per hour. How much distance did she travel?
Exercise 88
Mallory is taking the bus from St. Louis to Chicago. 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?
- Answer
-
5 hours
Exercise 89
Aaron’s friend drove him from Buffalo to Cleveland. The distance is 187 miles and the trip took 2.75 hours. How fast was Aaron’s friend driving?
Exercise 90
Link rode his bike at a steady rate of 15 miles per hour for 212 hours. How much distance did he travel?
- Answer
-
37.5 miles
Solve a Formula for a Specific Variable
In the following exercises, solve.
Exercise 91
Use the formula. d=rt to solve for t
- when d=510 and r=60
- in general
Exercise 92
Use the formula. d=rt to solve for r
- when when d=451 and t=5.5
- in general
- Answer
-
- r=82mph
- r=Dt
Exercise 93
Use the formula A=12bh to solve for b
- when A=390 and h=26
- in general
Exercise 94
Use the formula A=12bh to solve for b
- when A=153 and b=18
- in general
- Answer
-
- h=17
- h=2Ab
Exercise 95
Use the formula I=Prt to solve for the principal, P for
- I=$2,501,r=4.1%, t=5 years
- in general
Exercise 96
Solve the formula 4x+3y=6 for y
- when x=−2
- in general
- Answer
-
ⓐ y=143 ⓑ y=6−4x3
Exercise 97
Solve 180=a+b+c for c
Exercise 98
Solve the formula V=LWH for H
- Answer
-
H=VLW
Solve Linear Inequalities
Graph Inequalities on the Number Line
In the following exercises, graph each inequality on the number line.
Exercise 99
- x≤4
- x>−2
- x<1
Exercise 100
- x>0
- x<−3
- x≥−1
- Answer
-
In the following exercises, graph each inequality on the number line and write in interval notation.
Exercise 101
- x<−1
- x≥−2.5
- x≤54
Exercise 102
- x>2
- x≤−1.5
- x≥53
- Answer
-
Solve Inequalities using the Subtraction and Addition Properties of Inequality
In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation.
Exercise 103
n−12≤23
Exercise 104
m+14≤56
- Answer
-
Exercise 105
a+23≥712
Exercise 106
b−78≥−12
- Answer
-
Solve Inequalities using the Division and Multiplication Properties of Inequality
In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation.
Exercise 107
9x>54
Exercise 108
−12d≤108
- Answer
-
Exercise 109
52j<−60
Exercise 110
q−2≥−24
- Answer
-
Solve Inequalities That Require Simplification
In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation.
Exercise 111
6p>15p−30
Exercise 112
9h−7(h−1)≤4h−23
- Answer
-
Exercise 113
5n−15(4−n)<10(n−6)+10n
Exercise 114
38a−112a>512a+34
- Answer
-
Translate to an Inequality and Solve
In the following exercises, translate and solve. Then write the solution in interval notation and graph on the number line.
Exercise 115
Five more than z is at most 19.
Exercise 116
Three less than c is at least 360.
- Answer
-
Exercise 117
Nine times n exceeds 42.
Exercise 118
Negative two times a is no more than 8.
- Answer
-
Everyday Math
Exercise 119
Describe how you have used two topics from this chapter in your life outside of your math class during the past month.
Chapter 2 Practice Test
Exercise 1
Determine whether each number is a solution to the equation 6x−3=x+20
- 5
- 235
- Answer
-
- no
- yes
In the following exercises, solve each equation.
Exercise 2
n−23=14
Exercise 3
92c=144
- Answer
-
c=32
Exercise 4
4y−8=16
Exercise 5
−8x−15+9x−1=−21
- Answer
-
x=−5
Exercise 6
−15a=120
Exercise 7
23x=6
- Answer
-
x=9
Exercise 8
x−3.8=8.2
Exercise 9
10y=−5y−60
- Answer
-
y=−4
Exercise 10
8n−2=6n−12
Exercise 11
9m−2−4m−m=42−8
- Answer
-
m=9
Exercise 12
−5(2x−1)=45
Exercise 13
−(d−9)=23
- Answer
-
d=−14
Exercise 14
14(12m−28)=6−2(3m−1)
Exercise 15
2(6x−5)−8=−22
- Answer
-
x=−13
Exercise 16
8(3a−5)−7(4a−3)=20−3a
Exercise 17
14p−13=12
- Answer
-
p=103
Exercise 18
0.1d+0.25(d+8)=4.1
Exercise 19
14n−3(4n+5)=−9+2(n−8)
- Answer
-
contradiction; no solution
Exercise 20
9(3u−2)−4[6−8(u−1)]=3(u−2)
Exercise 21
Solve the formula x−2y=5 for y
- when x=−3
- in general
- Answer
-
- y=4
- y=5−x2
In the following exercises, graph on the number line and write in interval notation.
Exercise 22
x≥−3.5
Exercise 23
x<114
- Answer
-
In the following exercises,, solve each inequality, graph the solution on the number line, and write the solution in interval notation.
Exercise 24
8k≥5k−120
Exercise 25
3c−10(c−2)<5c+16
- Answer
-
In the following exercises, translate to an equation or inequality and solve.
Exercise 26
4 less than twice x is 16.
Exercise 27
Fifteen more than n is at least 48.
- Answer
-
n+15≥48;n≥33
Exercise 28
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?
Exercise 29
Jenna bought a coat on sale for $120, which was 23 of the original price. What was the original price of the coat?
- Answer
-
120=23p; The original price was $180
Exercise 30
Sean took the bus from Seattle to Boise, a distance of 506 miles. If the trip took 723 hours, what was the speed of the bus?
Review for 2.7 Ratio and Proportions and Similar Triangles
Solve Proportions
In the following exercises, solve.
Exercise 74
x4=35
- Answer
-
125
Exercise 75
3y=95
Exercise 76
ss+20=37
- Answer
-
15
Exercise 77
t−35=t+29
In the following exercises, solve using proportions.
Exercise 78
Rachael had a 21 ounce strawberry shake that has 739 calories. How many calories are there in a 32 ounce shake?
- Answer
-
1161 calories
Exercise 79
Leo went to Mexico over Christmas break and changed $525 dollars into Mexican pesos. At that time, the exchange rate had $1 US is equal to 16.25 Mexican pesos. How many Mexican pesos did he get for his trip?
In the following exercises, solve.
Exercise 80
∆ABC is similar to ∆XYZ. The lengths of two sides of each triangle are given in the figure. Find the lengths of the third sides.
- Answer
-
b=9; x=2\dfrac{1}{3}
Exercise \PageIndex{81}
On a map of Europe, Paris, Rome, and Vienna form a triangle whose sides are shown in the figure below. If the actual distance from Rome to Vienna is 700 miles, find the distance from
- a. Paris to Rome
- b. Paris to Vienna
Exercise \PageIndex{82}
Tony is 5.75 feet tall. Late one afternoon, his shadow was 8 feet long. At the same time, the shadow of a nearby tree was 32 feet long. Find the height of the tree.
- Answer
-
23 feet
Exercise \PageIndex{83}
The height of a lighthouse in Pensacola, Florida is 150 feet. Standing next to the statue, 5.5 foot tall Natalie cast a 1.1 foot shadow How long would the shadow of the lighthouse be?
Review for 2.9 Compound Inequalities
Solve Compound Inequalities with “and”
In each of the following exercises, solve each inequality, graph the solution, and write the solution in interval notation.
98. x\leq 5 and x>−3
- Answer
-
99. 4x−2\leq 4 and 7x−1>−8
100. 5(3x−2)\leq 5 and 4(x+2)<3
- Answer
-
101. 34(x−8)\leq 3 and 15(x−5)\leq 3
102. 34x−5\geq −2 and −3(x+1)\geq 6
- Answer
-
103. −5\leq 4x−1<7
Solve Compound Inequalities with “or”
In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation.
104. 5−2x\leq −1 or 6+3x\leq 4
- Answer
-
105. 3(2x−3)<−5 or 4x−1>3
106. 34x−2>4 or 4(2−x)>0
- Answer
-
107. 2(x+3)\geq 0 or 3(x+4)\leq 6
108. 12x−3\leq 4 or 13(x−6)\geq −2
- Answer
-
Solve Applications with Compound Inequalities
In the following exercises, solve.
109. Liam is playing a number game with his sister Audry. Liam is thinking of a number and wants Audry to guess it. Five more than three times her number is between 2 and 32. Write a compound inequality that shows the range of numbers that Liam might be thinking of.
110. Elouise is creating a rectangular garden in her back yard. The length of the garden is 12 feet. The perimeter of the garden must be at least 36 feet and no more than 48 feet. Use a compound inequality to find the range of values for the width of the garden.
- Answer
-
6\leq w\leq 12