Equations and Inequalities Test
Name: ___________________________________ Date:___________Period:_____
1. An equation is modeled.
What value of x makes the equation true?
A. 1
B. 7
C. -5
D. -1
2. Which situation is best represented by the following equation?
45𝑤 + 123.95 = 753.95
A. Ben paid $753.95 to join a gym. He paid a $123.95 registration fee and pays $45 for
each month of his membership. What is w, the number of months that he had the
membership?
B. Ben paid $753.95 to join a gym. He paid a $45 registration fee and pays $123.95 for
each month of his membership. What is w, the number of months that he had the
membership?
C. Ben and his brother paid $753.95 to join a gym. Ben paid a $123.95 each month of his
membership, and his brother paid $45 for each month of his membership. What is w,
the number of months that Ben and his brother had the membership?
D. Ben paid $753.95 to join a gym. He paid a $123.95 for each month that he was
enrolled at the gym after using a coupon that gave him $45 off for each month of his
membership. What is w, the number of months that he had the membership?
3. If 𝑥 = −5, which inequality is true?
A. −5 − 3𝑥 > 10
B. −3 − 5𝑥 < −15
C. 1 − 2𝑥 < 13
D. 2 − 𝑥 < −3
Equations and Inequalities Test
Name: ___________________________________ Date:___________Period:_____
4. Kayla and Brittany each have a lip gloss collection.
 The number of lip glosses in Kayla’s collection can be represented by x.
 The number of lip glosses in Brittany’s collection is four times the number in
Kayla’s collection.
 The total number of lip glosses in both collections is 160.
What is x, the number of lip glosses in Kayla’s collection?
A. 128
B. 40
C. 80
D. 32
5. What is the value of x, in the following equation.
2𝑥 + 4 = −52
Record your answer and fill in the bubbles on your answer document. Be sure to use the
correct place value.
6. Frankie’s dog weighs 4 pounds less than triple the weight of Cindy’s dog. Frankie’s dog
weighs 41 pounds. Which equation can be used to find, w, the weight of Cindy’s dog?
A. 41 = 3𝑤 + 4
B. 41 = 3𝑤 − 4
C. 𝑤 − 41 = 4
D. 𝑤 + 41 = 4
7. Which value of x makes the equation modeled below true?
A. 𝑥 = 2
B. 𝑥 = 6
C. 𝑥 = 8
D. 𝑥 = 10
8. Carrisa has $40 from her allowance. She spent $25.46 on a curling iron. She also wants to
buy bobby pins that cost $1.25 per package. Which inequality can be used to show how
many packs of bobby pins she can purchase, x, without exceeding her allowance?
A. 25.46 + 1.25 ≤ 40
B. 25.46 + 1.25𝑥 > 40
C. 25.46 + 1.25𝑥 ≤ 40
D. 25.46 + 1.25 ≥ 40
9. Which number line represents the solution to the inequality −2𝑥 + 5 > 19?
A.
B.
C.
D.
10. A store sells picture frames for $15 each. Photo prints sell for $0.35 each. Julie is buying
3 picture frames and x, photo prints. Which equation can be used to find y, the total price
Julie must pay in dollars?
A. 𝑦 = 0.35𝑥 + 15
B. 𝑦 = 0.35𝑥 + 45
C. 𝑦 = 15𝑥 + 0.35
D. 𝑦 = 45𝑥 + 0.35
11. Jeremy bought a bottle of Gatorade for $4. He also bought some hot dogs for $2.50
each. Jeremy did not spend more than $15 on the hot dogs and Gatorade. Which
inequality can be used to find h, the number of hot dogs that Jeremy could have bought?
A. 2.50ℎ − 4 ≤ 15
B. 2.50ℎ + 4 ≤ 15
C. 2.50ℎ − 4 ≥ 15
D. 2.50ℎ + 4 ≥ 15
Equations and Inequalities Test
Name: ___________________________________ Date:___________Period:_____
12.
Which of the following is the solution to the inequality below?
−5 + 3𝑥 < −68
13.
A. 𝑥 < 21
B. 𝑥 < −24
C. 𝑥 < 63
D. 𝑥 < −21
Julia, Alex, Mario, and Monica work together to solve the inequality below.
5𝑥 − 3 ≥ 17
None of the students agree on how to solve the inequality, though some of them arrived
at the same solution. Who has the correct process and solution for this inequality?
A. Julia says to add 3 to both sides and then divide by 5. The solution is 𝑥 = 4.
B. Alex says to subtract 3 from both sides and then divide by 5. The solution is 𝑥 = 4.
C. Mario says to subtract 3 from both sides and then divide by 5. The solution is 𝑥 ≥ 4.
D. Monica says to add 3 to both sides and then divide by 5. The solution is 𝑥 ≥ 4.
14.
Which situation could NOT be represented by the equation below?
600 − 30𝑤 = 250
A. Stefan wants to have $250 in his savings account at the end of the semester. He
begins with $600 in his account. If he withdraws $30 weekly, how many weeks
can Stefan withdraw and still meet his budget?
B. Derek has no more than $250 in his checking account. If he deposits $30 a week
and receives a bonus check of $600, how many weeks will it take to have more
than $600.
C. Kevin currently has $600 in his account. If he withdraws $30 a week, how many
weeks can Kevin withdraw money before his account balance is $250?
D. Eric opens a checking account with an initial deposit of $600. He needs $250
remaining in his account at the end of the year. If he transfers $30 from his
account each week, how many weeks will it be before Eric reaches an account
balance of $250?
Equations and Inequalities Test
Name: ___________________________________ Date:___________Period:_____
15.
What is the value of x, in the following equation.
−6𝑥 + 14 = 104
Record your answer and fill in the bubbles on your answer document. Be sure to use the
correct place value.
16.
Which of the following could be represented by the inequality below?
5𝑥 + 30 > 150
A. Sally makes bracelets to sell. Her profit for each bracelet sold is $5 and she has
already sold 30 bracelets. How many more bracelets must Sally sell is she wants to
make more than $150?
B. Sally makes bracelets to sell. Her profit for each bracelet is $5 and she has already
sold 30 bracelets. How many bracelets must Sally sell if she wants to make a
minimum of $150?
C. Sally makes bracelets to sell. Her profit for each bracelet is $5 and she has already
sold 6 bracelets. How many more must she sell if she wants to make more than
$150?
D. Sally makes bracelets to sell. Her profit for each bracelet is $5 and she has already
sold 6 bracelets. How many more must she sell if she wants to make a minimum of
$150?
17.
Which number line represents the solution to the inequality 4𝑥 + 27 > 15?
A.
B.
C.
D.
Equations and Inequalities Test
Name: ___________________________________ Date:___________Period:_____
18.
If 𝑥 = 6, which inequality is true?
A. 12 − 2𝑥 > 13
B. −4 − 5𝑥 > −15
C. 5 − 3𝑥 < −12
D. 10 − 𝑥 < −3
19. Regina wants to purchase a ticket for a concert. She will also purchase T-shirts for her
family. She is spending $50 for her ticket and knows that each shirt will cost $30. Which
inequality shows how many T-shirts could she purchase if she plans on spending a
maximum of $200?
20.
A. 𝑥 ≤ 5
B. 𝑥 < 5
C. 𝑥 > 5
D. 𝑥 ≥ 5
Which value of x makes the equation modeled below true?
A. 𝑥 = 2
B. 𝑥 = −1
C. 𝑥 = 5
D. 𝑥 = −2