AnswersSC-Mathematics 6Multiplication and Division Inequalities

Multiplication and Division Inequalities Answers

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A high school coach wants to buy new athletic shorts for the 15 members of the basketball team. The coach must spend less than $200 on the shorts. Which inequality represents the maximum cost of each pair, s, the coach can buy?

A
15 s less-than 200
Option A
B
15 s greater-than 200
Option B
C
15 s less-than-or-equal-to 200
Option C
D
15 s greater-than-or-equal-to 200
Option D
2
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Three-fourths of the employees at a bookstore came to a staff meeting. Less than 24 employees were at the meeting. The inequality representing this scenario is , where e represents the total number of employees. Which graph shows the solution to the inequality?

Question illustration
A
A number line going from 16 to 20. An open circle is at 18. Everything to the right of the circle is shaded.
Option A
B
A number line going from 16 to 20. An open circle is at 18. Everything to the left of the circle is shaded.
Option B
C
A number line going from 30 to 34. An open circle is at 32. Everything to the right of the circle is shaded.
Option C
D
A number line going from 30 to 34. An open circle is at 32. Everything to the left of the circle is shaded.
Option D
3

A sports club needs to raise at least $500 by selling chocolate bars for $2.50 each. Sebastian wants to know how many chocolate bars, c, the sports club must sell in order to reach its goal. Which of the following must be true about the inequality and the resulting graph? Select three options.

A
The inequality should be written as .
Option A
B
The inequality should be written as .
Option B
C
The circle is open.
D
The circle is closed.
E
The arrow points right.
4

Jose receives a $10 gift card for downloading music and wants to determine how many songs he can purchase. Each downloaded song costs $1.19. Write and solve an inequality to determine how many songs Jose can purchase. What does the solved inequality represent?

A
With the $10 gift card, Jose can buy at most 9 songs.
B
With the $10 gift card, Jose can buy 9 or more songs.
C
With the $10 gift card, Jose can buy at most 8 songs.
D
With the $10 gift card, Jose can buy 8 or more songs.
5

Two thirds of the employees at an office stated that they preferred soft cookies over crispy cookies. More than 36 employees stated their preference. Ren was asked to write, solve, and graph an inequality to find the number of employees working at the office. His work is shown below. Step Ren’s workStep 1Step 2Step 3Where, if any, did Ren first make a mistake in his work?

Question illustration
A
Step 1
B
Step 2
C
Step 3
D
No mistake found
6

A high school coach wants to buy new shirts for the 25 members of the track team. The coach must spend less than $300 on the shirts and needs to figure out how much he can spend per shirt, s. Which of the following must be true about the inequality and the resulting graph? Select three options.

A
The inequality should be written as .
Option A
B
The inequality should be written as .
Option B
C
The circle is open.
D
The circle is closed.
E
The arrow points left.
7

Max correctly solved this inequality.Which graph matches the inequality?

Question illustration
A
A number line going from negative 55 to negative 45. An open circle is at negative 50. Everything to the left of the line is shaded.
Option A
B
A number line going from negative 55 to negative 45. A closed circle is at negative 50. Everything to the left of the line is shaded.
Option B
C
A number line going from negative 55 to negative 45. An open circle is at negative 50. Everything to the right of the line is shaded.
Option C
D
A number line going from negative 55 to negative 45. A closed circle is at negative 50. Everything to the right of the line is shaded.
Option D
8

Jonas runs a pet store that sells guinea pigs. He wants to ensure he has more than 1 pound of dry food for every five guinea pigs he has in the store. He currently has 8 pounds of dry food and wants to know how many guinea pigs can he have in the store. Write and solve an inequality to solve this problem. What is the solution to the inequality?

A
x greater-than-or-equal-to 40
Option A
B
x less-than-or-equal-to 40
Option B
C
x greater-than-or-equal-to 8
Option C
D
x less-than-or-equal-to 8
Option D
9

A sports club needs to raise at least $240 by selling chocolate bars for $3.00 each. Sebastian wants to know how many chocolate bars, c, the sports club must sell in order to reach their goal. He represented this situation as . Which graph represents this inequality?

Question illustration
A
A number line going from 718 to 722. A closed circle is at 720. Everything to the right of the circle is shaded.
Option A
B
A number line going from 718 to 722. A closed circle is at 720. Everything to the left of the circle is shaded.
Option B
C
A number line going from 78 to 82. A closed circle is at 80. Everything to the right of the circle is shaded.
Option C
D
A number line going from 78 to 82. A closed circle is at 80. Everything to the left of the circle is shaded.
Option D
10

The table below shows an inequality and a number by which to divide both sides. InequalityDivide each side byWhat is the resulting true inequality?

Question illustration
A
Negative 25 less-than-or-equal-to negative 27
Option A
B
Negative 25 greater-than-or-equal-to negative 27
Option B
C
25 greater-than-or-equal-to 27
Option C
D
25 less-than-or-equal-to 27
Option D
11

Cecilia correctly solved this inequality.Which graph matches the inequality?

Question illustration
A
A number line going from 28 to 40. An open circle is at 34. Everything to the right of the circle is shaded.
Option A
B
A number line going from 28 to 40. An open circle is at 34. Everything to the left of the circle is shaded.
Option B
C
A number line going from 96 to 108. An open circle is at 102. Everything to the left of the circle is shaded.
Option C
D
A number line going from 96 to 108. An open circle is at 102. Everything to the right of the circle is shaded.
Option D
12

Max correctly solved this inequality.Which graph matches the inequality?

Question illustration
A
A number line going from negative 55 to negative 45. An open circle is at negative 50. Everything to the left of the line is shaded.
Option A
B
A number line going from negative 55 to negative 45. A closed circle is at negative 50. Everything to the left of the line is shaded.
Option B
C
A number line going from negative 55 to negative 45. An open circle is at negative 50. Everything to the right of the line is shaded.
Option C
D
A number line going from negative 55 to negative 45. A closed circle is at negative 50. Everything to the right of the line is shaded.
Option D
13

Owen runs a pet store that sells rabbits. He wants to ensure he has more than 1 pound of dry food for every four rabbits he has in the store, and he currently has 5.7 pounds of dry food. Write and solve an inequality for the scenario. How many rabbits can Owen have in the store?

A
Owen can have a minimum of 22 rabbits in the store.
B
Owen can have a maximum of 22 rabbits in the store.
C
Owen can have a maximum of 23 rabbits in the store.
D
Owen can have a minimum of 23 rabbits in the store.
14

Owen runs a pet store that sells rabbits. He wants to ensure he has more than 1 pound of dry food for every four rabbits he has in the store, and he currently has 5.7 pounds of dry food. Write and solve an inequality for the scenario. How many rabbits can Owen have in the store?

A
Owen can have a minimum of 22 rabbits in the store.
B
Owen can have a maximum of 22 rabbits in the store.
C
Owen can have a maximum of 23 rabbits in the store.
D
Owen can have a minimum of 23 rabbits in the store.
15

A sports club needs to raise at least $500 by selling chocolate bars for $2.50 each. Sebastian wants to know how many chocolate bars, c, the sports club must sell in order to reach its goal. Which of the following must be true about the inequality and the resulting graph? Select three options.

A
The inequality should be written as .
Option A
B
The inequality should be written as .
Option B
C
The circle is open.
D
The circle is closed.
E
The arrow points right.
16

Cecilia correctly solved this inequality.Which graph matches the inequality?

Question illustration
A
A number line going from 28 to 40. An open circle is at 34. Everything to the right of the circle is shaded.
Option A
B
A number line going from 28 to 40. An open circle is at 34. Everything to the left of the circle is shaded.
Option B
C
A number line going from 96 to 108. An open circle is at 102. Everything to the left of the circle is shaded.
Option C
D
A number line going from 96 to 108. An open circle is at 102. Everything to the right of the circle is shaded.
Option D
17

Mariya was asked to solve and then graph the solution. Her work is shown below. StepMariya’s work Step 1Step 2Step 3In which step, if any, did Mariya make a mistake in her work?

Question illustration
A
Step 1
B
Step 2
C
Step 3
D
No mistake found
18

A sports club needs to raise at least $240 by selling chocolate bars for $3.00 each. Sebastian wants to know how many chocolate bars, c, the sports club must sell in order to reach their goal. He represented this situation as . Which graph represents this inequality?

Question illustration
A
A number line going from 718 to 722. A closed circle is at 720. Everything to the right of the circle is shaded.
Option A
B
A number line going from 718 to 722. A closed circle is at 720. Everything to the left of the circle is shaded.
Option B
C
A number line going from 78 to 82. A closed circle is at 80. Everything to the right of the circle is shaded.
Option C
D
A number line going from 78 to 82. A closed circle is at 80. Everything to the left of the circle is shaded.
Option D
19

Solve the following inequality. Which graph shows the correct solution?

Question illustration
A
A number line going from 27 to 37. An open circle is at 32. Everything to the right of the circle is shaded.
Option A
B
A number line going from 27 to 37. An open circle is at 32. Everything to the left of the circle is shaded.
Option B
C
A number line going from 3 to 13. An open circle is at 8. Everything to the left of the circle is shaded.
Option C
D
A number line going from 3 to 13. An open circle is at 8. Everything to the right of the circle is shaded.
Option D
20

Three-fourths of the employees at a bookstore came to a staff meeting. Less than 24 employees were at the meeting. The inequality representing this scenario is , where e represents the total number of employees. Which graph shows the solution to the inequality?

Question illustration
A
A number line going from 16 to 20. An open circle is at 18. Everything to the right of the circle is shaded.
Option A
B
A number line going from 16 to 20. An open circle is at 18. Everything to the left of the circle is shaded.
Option B
C
A number line going from 30 to 34. An open circle is at 32. Everything to the right of the circle is shaded.
Option C
D
A number line going from 30 to 34. An open circle is at 32. Everything to the left of the circle is shaded.
Option D

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