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 1. 7n + 3.2 < 17.2
step 2. 7n < 14
step 3. n < 7
step 1. 7n + 3.2 < 17.2
step 2. 7n < 14
step 3. n < 7
Answers
GPT-4o mini
The student's solution has a small mistake in Step 2. Let's go through the steps to correctly solve the inequality.
We start with the given statement and inequality:
1. **Set up the inequality**: The statement "3.2 more than 7 times a number, \( n \), is less than 17.2" translates to the inequality:
\[
7n + 3.2 < 17.2
\]
2. **Subtract 3.2 from both sides**: To isolate the term with \( n \), we subtract 3.2 from both sides:
\[
7n < 17.2 - 3.2
\]
\[
7n < 14
\]
3. **Divide both sides by 7**: Now, we divide both sides by 7 to solve for \( n \):
\[
n < \frac{14}{7}
\]
\[
n < 2
\]
So the correct solution is \( n < 2 \). The mistake in the student’s work occurred in the final interpretation of the inequality; it should have concluded that \( n < 2 \), not \( n < 7 \).
We start with the given statement and inequality:
1. **Set up the inequality**: The statement "3.2 more than 7 times a number, \( n \), is less than 17.2" translates to the inequality:
\[
7n + 3.2 < 17.2
\]
2. **Subtract 3.2 from both sides**: To isolate the term with \( n \), we subtract 3.2 from both sides:
\[
7n < 17.2 - 3.2
\]
\[
7n < 14
\]
3. **Divide both sides by 7**: Now, we divide both sides by 7 to solve for \( n \):
\[
n < \frac{14}{7}
\]
\[
n < 2
\]
So the correct solution is \( n < 2 \). The mistake in the student’s work occurred in the final interpretation of the inequality; it should have concluded that \( n < 2 \), not \( n < 7 \).