Question
A teacher asks a student to write and solve an inequality to find what numbers satisfy the statement that 3.2 more than 7 times a number, n is less than 17.2 The table shows the student’s work.
step work
1 7n + 3.2 < 17.2
2 7n < 14
3 n < 7
Which statement is true?
Responses
A. The student’s work in all of the steps is correct because all numbers less than 7 satisfy the statement.
B. The student made a mistake writing the inequality before Step 1. The correct inequality that represents the statement is 3.2 n + 7 < 17.2 .
C. The student made a mistake between Step 1 and Step 2 by subtracting 3.2 from both sides of the inequality instead of adding 3.2 to both sides of the inequality.
D. The student made a mistake between Step 1 and Step 3 by subtracting 7 from the right side of the inequality instead of dividing both sides of the inequality by 7
step work
1 7n + 3.2 < 17.2
2 7n < 14
3 n < 7
Which statement is true?
Responses
A. The student’s work in all of the steps is correct because all numbers less than 7 satisfy the statement.
B. The student made a mistake writing the inequality before Step 1. The correct inequality that represents the statement is 3.2 n + 7 < 17.2 .
C. The student made a mistake between Step 1 and Step 2 by subtracting 3.2 from both sides of the inequality instead of adding 3.2 to both sides of the inequality.
D. The student made a mistake between Step 1 and Step 3 by subtracting 7 from the right side of the inequality instead of dividing both sides of the inequality by 7
Answers
GPT-4o mini
Let's analyze the student's work step by step:
1. **Step 1**: The student wrote the inequality as \( 7n + 3.2 < 17.2 \). This part is correct according to the problem statement, as it correctly represents "3.2 more than 7 times a number n is less than 17.2".
2. **Step 2**: The student continued with \( 7n < 14 \). To reach this step, they correctly subtracted 3.2 from both sides of the inequality in Step 1. Specifically:
\[
7n + 3.2 < 17.2
\]
would become
\[
7n < 17.2 - 3.2
\]
which simplifies to:
\[
7n < 14
\]
This step is also correct.
3. **Step 3**: Finally, the student wrote \( n < 7 \). Here, they should have divided both sides of the inequality \( 7n < 14 \) by 7 to isolate \( n \):
\[
n < \frac{14}{7} \rightarrow n < 2
\]
Hence, this step contains a mistake because \( n < 7 \) is not correct.
Considering the options:
A. The student’s work in all of the steps is correct because all numbers less than 7 satisfy the statement. **(Incorrect)**
B. The student made a mistake writing the inequality before Step 1. The correct inequality that represents the statement is \( 3.2n + 7 < 17.2 \). **(Incorrect)**
C. The student made a mistake between Step 1 and Step 2 by subtracting 3.2 from both sides of the inequality instead of adding 3.2 to both sides of the inequality. **(Incorrect)**
D. The student made a mistake between Step 1 and Step 3 by subtracting 7 from the right side of the inequality instead of dividing both sides of the inequality by 7. **(Correct)**
Thus, the correct answer is **D**.
1. **Step 1**: The student wrote the inequality as \( 7n + 3.2 < 17.2 \). This part is correct according to the problem statement, as it correctly represents "3.2 more than 7 times a number n is less than 17.2".
2. **Step 2**: The student continued with \( 7n < 14 \). To reach this step, they correctly subtracted 3.2 from both sides of the inequality in Step 1. Specifically:
\[
7n + 3.2 < 17.2
\]
would become
\[
7n < 17.2 - 3.2
\]
which simplifies to:
\[
7n < 14
\]
This step is also correct.
3. **Step 3**: Finally, the student wrote \( n < 7 \). Here, they should have divided both sides of the inequality \( 7n < 14 \) by 7 to isolate \( n \):
\[
n < \frac{14}{7} \rightarrow n < 2
\]
Hence, this step contains a mistake because \( n < 7 \) is not correct.
Considering the options:
A. The student’s work in all of the steps is correct because all numbers less than 7 satisfy the statement. **(Incorrect)**
B. The student made a mistake writing the inequality before Step 1. The correct inequality that represents the statement is \( 3.2n + 7 < 17.2 \). **(Incorrect)**
C. The student made a mistake between Step 1 and Step 2 by subtracting 3.2 from both sides of the inequality instead of adding 3.2 to both sides of the inequality. **(Incorrect)**
D. The student made a mistake between Step 1 and Step 3 by subtracting 7 from the right side of the inequality instead of dividing both sides of the inequality by 7. **(Correct)**
Thus, the correct answer is **D**.