WorksheetsExpressions Equations and Inequalities Review
Total questions: 44
Worksheet time: 2hrs 41mins
Name
Class
Date
1.
1 + 9a - 8 = 8a
a)
a = 7
b)
all real numbers
c)
no solution
d)
a = =9
2.
6(5g+ 2)=30g
a)
g=2
b)
g=12
c)
all real numbers
d)
no solution
3.
5(2x -1) = -5+ 10x
a)
x = 5
b)
x = 0
c)
all real numbers
d)
no solution
4.
Solve for x:
4(1 - x) + 3x = - 2(x + 1)
4(1 - x) + 3x = - 2(x + 1)
a)
x = -6
b)
x = 6
c)
x = 3
5.
Solve:
2(4x - 3) - 8 = 4 + 2x
2(4x - 3) - 8 = 4 + 2x
a)
x = 5/3
b)
x = 3
c)
x = 1
d)
x = 2
6.
Solve: -1/3(x+6)=19
a)
63
b)
-7
c)
-63
d)
14
7.
a)
5
b)
-45
c)
-5
d)
4
8.
Solve:
8m - 9 > 71
8m - 9 > 71
a)
m > 10
b)
m > 1
c)
m < 1
d)
m > -48
9.
Solve:
8 - 3k < 8(1 - 7k)
8 - 3k < 8(1 - 7k)
a)
k < 5
b)
k > 5
c)
k < -33
d)
k < 0
10.
Which is a solution of
5(v + 3) - 10v > -10
5(v + 3) - 10v > -10
a)
v < 5
b)
v > 5
c)
v > -5
d)
v < -5
11.
What inequality does the number line graph represent?
a)
x + 4 ≤ -1
b)
2x - 3 < 7
c)
x - 1 ≤ 4
d)
2x + 3 >13
12.
Which number line shows the solution set to the inequality below?
x - 3 > -3
x - 3 > -3
a)
A
b)
B
c)
C
d)
D
13.
-5(1 - 4a) > -5
a)
a > 0
b)
a < 5
c)
a < 0
d)
a > 5
14.
solve the following inequality
5-(4x -5) ≤ 30
5-(4x -5) ≤ 30
a)
x ≤ -5
b)
x < 10
c)
x ≥ -5
d)
x ≥ 10
15.
solve 5( 6 + 3r) + 7 ≥ 127
a)
r ≤ 6
b)
r ≥ 6
c)
r ≤ -6
d)
r ≥ -6
16.
Mallory bought pizza and soda for a party. If she spent $12.57 on the sodas and $10.95 for each pizza, how many pizzas did she buy if her total is $89.22?
a)
10.95x + 12.57 = 89.22
b)
12.57x + 10.95 = 89.22
c)
89.22x -10.95 = 12.57
d)
12.57 + 10.95 = 89.22
17.
Jen wants to buy a new car for $18500. She pays $2500 at signing and wants to pay $250 per month. How many months until it is paid off?
a)
18500 + 2500 = 250x
b)
2500 -250x = 18500
c)
250x + 2500 = 18500
d)
2500(250)x = 18500
18.
Your cell phone bill is $21.20. The company charges $0.25 per call.
a)
0.25c = 21.20
b)
c - 0.25 = 21.20
c)
c + 0.25 = 21.20
d)
0.25 ÷ c = 21.20
19.
There were 331 students that went on a field trip. Six buses were filled and 7 students traveled in a van. How many students were on each bus?
a)
6 + 7x = 331
b)
331 - 6x = 7
c)
6x + 7 = 331
20.
Mark works 3 hours on Friday and 5 hours on Saturday. He gets a weekly allowance of $25. If he had $85 this week, how much does he get paid an hour?
a)
8x + 25 = 85
b)
3x + 5x = 25
c)
85 - 25 = 8x
21.
Mei was going to sell all of her stamp collection to buy a video game. After selling half of them she changed her mind. She then bought nineteen more. How many did she start with if she now has 45?
a)
2/x + 19 = 90
b)
x/2 + 19 = 45
c)
2x +19 = 109
d)
19x + 2 = 71
22.
Natalie is a softball coach. She has a pitching private lesson with Kasey. Kasey's mom pays Natalie $11 per hour plus a $6 tip. Write an equation that represents the number of hours (h) of lessons Kasey took if the total cost was $39.
a)
11 + 6h = 39
b)
11h - 6 = 39
c)
11h + 6 = 39
d)
66h = 39
23.
Penelope is going to the carnival to ride the rides. It costs $20 to get into the carnival and ride tickets are $0.50 each. Write an equation that represents the number of tickets (t) that can be purchased if Penelope plans to spend $35.
a)
.50t + 20 = 35
b)
.50t = 35
c)
.50 + 20t = 35
d)
.50t +35 = 20
24.
An electrician charges $90 per hour along with a $60 traveling fee. If your bill was $600, write an equation that can be used to determine how many hours (h) it took the electrician to complete the job.
a)
60 - 90h=600
b)
90h + 60 = 600
c)
60h + 90 = 600
d)
60h - 600 = 90
25.
Ms. Jacobs is a photographer . For each job she charges $135 for the first hour she works and $100 for each additional hour. Ms. Jacobs charged $535 for a job she completed. Write an equation that can be used to determine the number of hours (h) she spent on the job.
a)
135x + 100 = 535
b)
100x - 135 = 535
c)
100x + 135 = 535
d)
135x - 100 = 535
26.
The vet told Casey that her dog should weigh at most 70 lbs. Her dog weighs 106 pounds, so Casey set a goal that he would lose 4 pounds per week. Which inequality represents the number of weeks it take for Casey's dog to reach 70 lbs?
a)
106 - 4x ≤ 70
b)
70 + 4x ≤ 106
c)
4x - 106 ≥ 70
d)
106 - 4x< 70
27.
The members of Carver Middle School's Junior Beta Club need to raise at least $2000 to attend their national convention. They raised $300 with their last fundraiser and decide to host a school talent show to raise the rest. They plan to charge $10 for each ticket. Which inequality shows the number of tickets they must sale to reach their goal?
a)
300x + 10 ≥ 2000
b)
10x + 300 ≤ 2000
c)
10x + 300 > 2000
d)
10x + 300 ≥ 2000
28.
Juan bought a soda for $2. He also bought some nachos for $3 each. Juan did not spend more than $14 on the nachos and the soda. Write an inequality can be used to find n, the number of nachos that Juan could have bought.
a)
14≥2n+3
b)
2+3n≤14
c)
14-3n≤2
29.
The booster club needs to raise at least $7,000 for new football uniforms. So far, they have raised $1,250. Write an inequality to find the average amounts each of the 92 members can raise to meet the club’s objective.
a)
1,250 + 92x > 7,000
b)
1,250 + 92x ≥ 7,000
c)
1,250 + 92x ≤ 7,000
d)
1,250 + 92x < 7,000
30.
Gabby has $14 and plans to save $5 each week until she has the $64 she needs for a new jacket. How many weeks will it take Gabby to save money for a new jacket?
a)
11 weeks
b)
10 weeks
c)
12 weeks
d)
13 weeks
31.
A computer printer can print 10 pages per minute. There were already 35 pages in the tray. The total pages printed was 115 pages. How many minutes has the printer been running?
a)
8
b)
9
c)
7
d)
10
32.
Jared made sixty dollars mowing lawns over the summer. If he spent thirty-nine dollars buying new mower blades, how many seven dollar games could he buy with the money he had left?
a)
21 games
b)
3 games
c)
7 games
d)
99 games
33.
To qualify for an award, a student volunteers no less than 5 hours each week at the local hospital. Write an inequality that represents how many hours the student volunteers each week.
a)
X < 5
b)
X > 5
c)
X ≥ 5
d)
X ≤ 5
34.
The admission fee to an arcade is $1.25 per person and it costs $.50 for each game played. Joey has $10 from his allowance to spend. Which inequality represents Joey getting the most out his $10 allowance.
a)
1.25+.50g ≤ 10
b)
1.25-.50g ≤ 10
c)
1.25+.50g ≥ 10
d)
1.25- .50g ≥ 10
35.
3. Keith has $500 in a savings account at the beginning of the summer. He wants to have at least $200 at the end of the summer. He withdraws $25 per week for food, clothing, and movie tickets. How many weeks can Keith withdraw money from his account?
a)
16 weeks
b)
14 weeks
c)
12 weeks
d)
10 weeks
36.
Half of your baseball card collection got wet & was ruined. You bought 19 cards to replace some that were lost. How many did you begin with if you now have 45?
a)
13
b)
26
c)
52
d)
87
37.
Which situation can be represented by the equation:
800 + 25x > 1280 - 15x
800 + 25x > 1280 - 15x
a)
At the beginning of the year, Mark has $800 in his savings account and Brooke has $1,280 in her savings account. Each month, Mark deposits an additional $25 in his account, while Brooke withdraws $15 from her account. Write an equation to show after how many months will Brooke's account have a greater balance than Mark’s account?
b)
At the beginning of the year, Mark has $800 in his savings account and Brooke has $1,280 in her savings account. Each month, Mark deposits an additional $25 in his account, while Brooke withdraws $15 from her account. Write an equation to show after how many months will Mark’s account have a greater balance than Brooke’s account?
c)
At the beginning of the year, Mark has $800 in his savings account and Brooke has $1,280 in her savings account. Each month, Mark deposits an additional $25 in his account, while Brooke withdraws $15 from her account. Write an equation to show after how many months will Mark’s account the same balance as Brooke’s account?
d)
At the beginning of the year, Mark has $800 in his savings account and Brooke has $1,280 in her savings account. Each month, Mark withdraws $25 from his account, while Brooke deposits $15 into her account. Write an equation to show after how many months will Mark’s account have a greater balance than Brooke’s account?
38.
Which situation can be represented by the equation:
15 + 3x = 21 + x
15 + 3x = 21 + x
a)
Peppy Pets charges a flat fee of $3 plus $15 per hour to keep a dog during the day. Happy Hounds charges a flat fee of $1 plus $21 per hour. For how many hours is the total fee charged by the companies the same?
b)
Peppy Pets charges a flat fee of $15 plus $3 per hour to keep a dog during the day. Happy Hounds charges a flat fee of $21 plus $1 per hour. For how many hours is Peppy Pets going to cost more than Happy Hounds?
c)
Peppy Pets charges a flat fee of $15 plus $3 per hour to keep a dog during the day. Happy Hounds charges a flat fee of $21 plus $1 per hour. For how many hours is the total fee charged by the companies the same?
d)
Peppy Pets charges a flat fee of $15 plus $3 per hour to keep a dog during the day. Happy Hounds charges a flat fee of $21 plus $1 per hour. For how many hours is Peppy Pets going to cost less than Happy Hounds?
39.
Which situation can be represented by the equation:
25 - 2.5d > 50 - 3.25d
25 - 2.5d > 50 - 3.25d
a)
Sue's lunch account has $25 and she spends $2.50 every day. Troy's lunch account has $50 and she spends $3.25 every day. How many days will it take for Sue's account will be less than Troy's?
b)
Sue's lunch account has $25 and she spends $2.50 every day. Troy's lunch account has $50 and she spends $3.25 every day. How many days will it take for Sue's account will be more than Troy's?
c)
Sue's lunch account has $50 and she spends $3.25 every day. Troy's lunch account has $25 and she spends $2.50 every day. How many days will it take for Sue's account to be more than Troy's?
d)
Sue's lunch account has $25 and she spends $2.50 every day. Troy's lunch account has $50 and she spends $3.25 every day. How many days will it take for Sue's account to be the same as Troy's?
40.
Which situation can be represented by the equation:
2x +15 = 3x + 5
2x +15 = 3x + 5
a)
Clean Fast Window Cleaner Company charges $3 per window plus a $15 fee. See Out Window Cleaner Company charges $2 per window plus a $5 fee. How many windows will it take for Clean Fast to cost the same as See Out?
b)
Clean Fast Window Cleaner Company charges $3 per window plus a $15 fee. See Out Window Cleaner Company charges $2 per window plus a $5 fee. How many windows will it take for Clean Fast to cost more than See Out?
c)
Clean Fast Window Cleaner Company charges $3 per window plus a $15 fee. See Out Window Cleaner Company charges $2 per window plus a $5 fee. How many windows will it take for Clean Fast to cost less than See Out?
d)
Clean Fast Window Cleaner Company charges $2 per window plus a $15 fee. See Out Window Cleaner Company charges $3 per window plus a $5 fee. How many windows will it take for Clean Fast to cost the same as See Out?
41.
You and your sister help your neighbor rake their lawn. Your sister can rake at a rate of 2 square meters per minute, and you can rake at a rate of 4 square meters per minute. You start at the same time. After how many minutes will you rake 8 square meters more than your sister?
a)
m=8
b)
m=4
c)
m=10
d)
m=6
42.
You ride an express bus from the center of town to your street. You have two payment options. Option A is to buy a monthly pass and pay $0.80 per ride. Option B is to pay $2.30 per ride. A monthly pass costs $30. After how many rides will the total costs of the two options be the same?
a)
r=20 rides
b)
r=10 rides
c)
r=15 rides
d)
r=25 rides
43.
You play basketball in your school’s indoor stadium. You have two payment options. Option A is to buy a membership card and pay $2 each time you go to the gym. Option B is to pay $4 each time you go. A membership card costs $20. After how many times will the cost of Option A be equal to the cost of Option B?
a)
t=5 times
b)
t=7 times
c)
t=10 times
d)
t=13 times
44.
At one gym, there is a $12 start-up fee, and after that each month at the gym costs $20. At another gym, it costs $4 to startup, but after that, each month at the gym costs $22. After how many months will the cost of both gyms be the same?
a)
m = 1 month
b)
m= 2 months
c)
m= 3 months
d)
m= 4 months
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