Question 1

Question

Question 1

A)Solve x+15≥3. Make sure to write your inequality so that x comes first.(1 point)
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Question 2
A)Solve x+212<8. Make sure to write your inequality so that x comes first.(1 point)
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Question 3
A)
Use the image to answer the question.

A number line with arrows at both the ends ranges from negative 10 to 10 in unit increments. An open circle is marked on the number line at 4.5. A line is drawn from the circle toward negative 10 with an arrow at the end.

Willow solved an inequality and graphed the solution on the number line. Which of the following inequalities did she solve?

(1 point)
Responses

x+1.25≤5.75
x plus 1.25 less-than-or-equal-to 5.75

x+212<212
x plus 2 Start Fraction 1 over 2 End Fraction less than 2 Start Fraction 1 over 2 End Fraction

x−1.5≤3
x minus 1.5 less-than-or-equal-to 3

x−213<216
x minus 2 Start Fraction 1 over 3 End Fraction less than 2 Start Fraction 1 over 6 End Fraction
Question 4
A)Solve 5x<12. Write the improper fraction in your answer as a mixed number. Make sure to write your inequality so that x comes first.(1 point)
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Question 5
A)Solve 3.4x≥23.8. Make sure to write your inequality so that x comes first.(1 point)
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Question 6
A)
Use the image to answer the question.

A number line ranges from negative 10 to 10 with numbers listed in unit increments. An open point is plotted on the number line at 4. A leftward arrow is marked on the number line that originates at the open circle and goes beyond negative 10.

Paolo solved an inequality and graphed the solution on the number line. Which of the following inequalities did he solve?

(1 point)
Responses

3.7x>14.8
3.7 x greater than 14.8

2.1x<8.4
2.1 x less than 8.4

4.9x>19.6
4.9 x greater than 19.6

2.8x<10.5
2.8 x less than 10.5
Question 7
A)Solve 8x−14≤10. Make sure to write your inequality so that x comes first.(1 point)
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Question 8
A)Solve 5.14x+2.25>15.1. Write the rational number in your answer in decimal form to the tenths place. Make sure to write your inequality so that x comes first.(1 point)
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Question 9
A)
Use the image to answer the question.

A number line is shown ranging from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line between 1 and 2. A rightward arrow is marked on the number line that originates at the closed point and goes beyond 10.

Preston solved an inequality and graphed the solution on the number line. Which of the following inequalities did he solve?

(1 point)
Responses

2.1x+5.6≥8.75
2.1 x plus 5.6 greater than or equal to 8.75

3.4x−1.2≥4.75
3.4 x minus 1.2 greater than or equal to 4.75

5.6x−18.9≤0.7
5.6 x minus 18.9 less than or equal to 0.7

0.9x+2.8≤5.95
0.9 x plus 2.8 less than or equal to 5.95
Question 10
A)Fifteen less than four times a number is more than 49. What are all the possible values of the number? Write an inequality that could be used to solve this problem. Use the letter x as your variable and write your x term first.(1 point)
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Question 11
A)Youssef is taking a trip on an airplane. He knows that to avoid extra fees his suitcase must weigh under 50 pounds. The suitcase with his clothes weighs 35 pounds. He has room, so he decides to pack some books for his trip, too. Each book weighs on average 1.2 pounds. He writes the inequality 1.2b+35<50, where b equals the number of books, to help figure this out. Solve his inequality. Use the letter b as your variable and write your b term first. After solving the inequality, use your answer to determine how many whole books Youssef can bring on his trip.(1 point)
Youssef can bring $$ books.
Question 12
A)Marjam has a goal of taking at least 10,000 steps today. According to her pedometer, she got 2,500 steps in the morning. There are 10 hours left in the day. How many steps will she need to get each hour (assume she walks the same number of steps each hour) for the rest of the day to meet her goal? Solve this problem. Which graph most clearly communicates the solution?(1 point)
Responses

An illustration shows a number line labeled Marjam’s Steps per Hour for the Remainder of the Day. The number line ranges from 0 to 900 in 100 unit increments. A closed point is plotted at 750. A line extends from that point to the right and goes past 900.
Image with alt text: An illustration shows a number line labeled Marjam’s Steps per Hour for the Remainder of the Day. The number line ranges from 0 to 900 in 100 unit increments. A closed point is plotted at 750. A line extends from that point to the right and goes past 900.

A number line ranges from 0 to 900 in 100 unit increments. An open point is labeled and plotted at 750. A line extends from that point to the right and goes past 900.
Image with alt text: A number line ranges from 0 to 900 in 100 unit increments. An open point is labeled and plotted at 750. A line extends from that point to the right and goes past 900.

A number line ranges from 0 to 900 in 100 unit increments. An open point is labeled and plotted at 750. A line extends from that point to the right and goes past 900.
Image with alt text: A number line ranges from 0 to 900 in 100 unit increments. An open point is labeled and plotted at 750. A line extends from that point to the right and goes past 900.

A number line is marked with 10 equidistant tick marks. An open point is plotted halfway between the eighth and ninth tick marks from the left. A line extends from that point to the right and goes past the last tick mark.
Image with alt text: A number line is marked with 10 equidistant tick marks. An open point is plotted halfway between the eighth and ninth tick marks from the left. A line extends from that point to the right and goes past the last tick mark.
Question 13
A)
Use the image to answer the question.

A number line ranges from 16 to 32 in 1 unit increments. An open point is labeled and plotted at 25.60. A line extends from that point to the right and goes past 32. The number line is labeled Bogdan's Earnings Per Yard.

What inequality is shown on the graph? Write your inequality with the variable coming first. Use the letter m for the variable. Write your answer using a decimal number.

(1 point)
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Question 14
A)Lily is saving up to buy a cellphone. She needs to save at least $300 before she is able to buy the phone. Her grandfather gives her $40, and she earns $65 tutoring after school each week. Write an inequality for the number of weeks Lily will need to save to have at least $300, and describe the solutions.(2 points)
$$x+ $$ ≥$$, where x is the number of weeks Lily will need to save. Lily must save for at least $$ weeks to have at least $300.
Question 15
A)Solve this problem by writing and solving an inequality. Five more than four times a number is less than 25. What are the possible values of the number? Show your work. (4 points)

Math Short Answer Rubric (4 points)
Points Awarded Criteria
4
The answer is clear and correct.

The answer shows that the student used problem-solving skills and reasoning.

All work is shown or explained.

3
The answer is mostly correct. The student made small errors while solving.

The answer shows that the student used some problem-solving skills and reasoning.

Most work is shown or explained.

2
The answer is partially correct. The student made errors while solving.

The answer shows that the student used some problem-solving skills or reasoning.

Some work is shown or explained.

1
The answer is incorrect. The student made errors while solving.

The answer shows little problem-solving skills or reasoning.

Little or no work is shown.

0 The question is not answered.
with summary of anwsers at the end

1 answer

Sure! Here are the solutions for each question:

Question 1

A) Solve $ x + 15 \geq 3 $: \[ x \geq 3 - 15 \quad \Rightarrow \quad x \geq -12 \] Answer: $ x \geq -12 $

Question 2

A) Solve $ x + 212 < 8 $: \[ x < 8 - 212 \quad \Rightarrow \quad x < -204 \] Answer: $ x < -204 $

Question 3

A) Willow's graph shows an open circle at 4.5 with a line extending to the left (indicating a "less than" relationship). Therefore, she solved: Response: $ x + 1.25 < 5.75 $

Question 4

A) Solve $ 5x < 12 $: \[ x < \frac{12}{5} \quad \Rightarrow \quad x < 2.4 \] Answer: $ x < 2.4 $

Question 5

A) Solve $ 3.4x \geq 23.8 $: \[ x \geq \frac{23.8}{3.4} \approx 7 \] Answer: $ x \geq 7 $

Question 6

A) Paolo's graph shows an open circle at 4 with a line extending left. Thus, he solved: Response: $ 2.1x < 8.4 $

Question 7

A) Solve $ 8x - 14 \leq 10 $: \[ 8x \leq 10 + 14 \quad \Rightarrow \quad 8x \leq 24 \quad \Rightarrow \quad x \leq 3 \] Answer: $ x \leq 3 $

Question 8

A) Solve $ 5.14x + 2.25 > 15.1 $: \[ 5.14x > 15.1 - 2.25 \quad \Rightarrow \quad 5.14x > 12.85 \quad \Rightarrow \quad x > \frac{12.85}{5.14} \approx 2.5 \] Answer: $ x > 2.5 $

Question 9

A) Preston's graph indicates a closed point with a line extending right, suggesting he solved: Response: $ 3.4x - 1.2 \geq 4.75 $

Question 10

A) "Fifteen less than four times a number is more than 49": \[ 4x - 15 > 49 \quad \Rightarrow \quad 4x > 64 \quad \Rightarrow \quad x > 16 \] Answer: $ 4x - 15 > 49 $

Question 11

A) $ 1.2b + 35 < 50 $: \[ 1.2b < 50 - 35 \quad \Rightarrow \quad 1.2b < 15 \quad \Rightarrow \quad b < \frac{15}{1.2} \approx 12.5 \] Answer: Youssef can bring 12 books (the whole number).

Question 12

A) Total steps needed: $ 10,000 - 2,500 = 7,500 $ steps over 10 hours: \[ \frac{7500}{10} = 750 \text{ steps per hour} \] Graph: The number line labeled with 750 as a closed point extending right.

Question 13

A) The graph has an open point at 25.60 and extends right: \[ m > 25.6 \] Answer: $ m > 25.6 $

Question 14

A) Let $ x $ be the number of weeks needed: \[ 65x + 40 \geq 300 \quad \Rightarrow \quad 65x \geq 260 \quad \Rightarrow \quad x \geq 4 \] Answer: $ x + 40 \geq 300, \text{ Lily must save for at least } 4 \text{ weeks.} $

Question 15

A) "Five more than four times a number is less than 25": \[ 4x + 5 < 25 \quad \Rightarrow \quad 4x < 20 \quad \Rightarrow \quad x < 5 \] Answer: $ 4x + 5 < 25 $

Summary of Answers:

$ x \geq -12 $
$ x < -204 $
$ x + 1.25 < 5.75 $
$ x < 2.4 $
$ x \geq 7 $
$ 2.1x < 8.4 $
$ x \leq 3 $
$ x > 2.5 $
$ 3.4x - 1.2 \geq 4.75 $
$ 4x - 15 > 49 $
Youssef can bring 12 books.
Steps per hour: 750
$ m > 25.6 $
$ x + 40 \geq 300, 4 \text{ weeks}$
$ 4x + 5 < 25 $

Feel free to ask for clarifications or more information on any question!

GPT-4o mini · Answer

Sure! Here are the solutions for each question:

Question 1

A) Solve $ x + 15 \geq 3 $: \[ x \geq 3 - 15 \quad \Rightarrow \quad x \geq -12 \] Answer: $ x \geq -12 $

Question 2

A) Solve $ x + 212 < 8 $: \[ x < 8 - 212 \quad \Rightarrow \quad x < -204 \] Answer: $ x < -204 $

Question 3

A) Willow's graph shows an open circle at 4.5 with a line extending to the left (indicating a "less than" relationship). Therefore, she solved: Response: $ x + 1.25 < 5.75 $

Question 4

A) Solve $ 5x < 12 $: \[ x < \frac{12}{5} \quad \Rightarrow \quad x < 2.4 \] Answer: $ x < 2.4 $

Question 5

A) Solve $ 3.4x \geq 23.8 $: \[ x \geq \frac{23.8}{3.4} \approx 7 \] Answer: $ x \geq 7 $

Question 6

A) Paolo's graph shows an open circle at 4 with a line extending left. Thus, he solved: Response: $ 2.1x < 8.4 $

Question 7

A) Solve $ 8x - 14 \leq 10 $: \[ 8x \leq 10 + 14 \quad \Rightarrow \quad 8x \leq 24 \quad \Rightarrow \quad x \leq 3 \] Answer: $ x \leq 3 $

Question 8

A) Solve $ 5.14x + 2.25 > 15.1 $: \[ 5.14x > 15.1 - 2.25 \quad \Rightarrow \quad 5.14x > 12.85 \quad \Rightarrow \quad x > \frac{12.85}{5.14} \approx 2.5 \] Answer: $ x > 2.5 $

Question 9

A) Preston's graph indicates a closed point with a line extending right, suggesting he solved: Response: $ 3.4x - 1.2 \geq 4.75 $

Question 10

A) "Fifteen less than four times a number is more than 49": \[ 4x - 15 > 49 \quad \Rightarrow \quad 4x > 64 \quad \Rightarrow \quad x > 16 \] Answer: $ 4x - 15 > 49 $

Question 11

A) $ 1.2b + 35 < 50 $: \[ 1.2b < 50 - 35 \quad \Rightarrow \quad 1.2b < 15 \quad \Rightarrow \quad b < \frac{15}{1.2} \approx 12.5 \] Answer: Youssef can bring 12 books (the whole number).

Question 12

A) Total steps needed: $ 10,000 - 2,500 = 7,500 $ steps over 10 hours: \[ \frac{7500}{10} = 750 \text{ steps per hour} \] Graph: The number line labeled with 750 as a closed point extending right.

Question 13

A) The graph has an open point at 25.60 and extends right: \[ m > 25.6 \] Answer: $ m > 25.6 $

Question 14

A) Let $ x $ be the number of weeks needed: \[ 65x + 40 \geq 300 \quad \Rightarrow \quad 65x \geq 260 \quad \Rightarrow \quad x \geq 4 \] Answer: $ x + 40 \geq 300, \text{ Lily must save for at least } 4 \text{ weeks.} $

Question 15

A) "Five more than four times a number is less than 25": \[ 4x + 5 < 25 \quad \Rightarrow \quad 4x < 20 \quad \Rightarrow \quad x < 5 \] Answer: $ 4x + 5 < 25 $

Summary of Answers:

$ x \geq -12 $
$ x < -204 $
$ x + 1.25 < 5.75 $
$ x < 2.4 $
$ x \geq 7 $
$ 2.1x < 8.4 $
$ x \leq 3 $
$ x > 2.5 $
$ 3.4x - 1.2 \geq 4.75 $
$ 4x - 15 > 49 $
Youssef can bring 12 books.
Steps per hour: 750
$ m > 25.6 $
$ x + 40 \geq 300, 4 \text{ weeks}$
$ 4x + 5 < 25 $

Feel free to ask for clarifications or more information on any question!