Question

Paolo solved an inequality and graphed the solution on the number line. Which of the following inequalities did he solve? (1 point) Responses 4.9x>19.6 4.9 x greater than 19.6 2.1x<8.4 2.1 x less than 8.4 3.7x>14.8 3.7 x greater than 14.8 2.8x<10.5

Answer 1

To determine which inequality Paolo solved, we need to analyze each option closely, potentially calculating the value of \( x \) in each case.

1. **For the inequality \( 4.9x > 19.6 \)**:
- Divide both sides by 4.9:
\[
x > \frac{19.6}{4.9} = 4
\]

2. **For the inequality \( 2.1x < 8.4 \)**:
- Divide both sides by 2.1:
\[
x < \frac{8.4}{2.1} = 4
\]

3. **For the inequality \( 3.7x > 14.8 \)**:
- Divide both sides by 3.7:
\[
x > \frac{14.8}{3.7} \approx 4
\]

4. **For the inequality \( 2.8x < 10.5 \)**:
- Divide both sides by 2.8:
\[
x < \frac{10.5}{2.8} \approx 3.75
\]

Now summarizing the results:
- \( 4.9x > 19.6 \) gives the solution \( x > 4 \)
- \( 2.1x < 8.4 \) gives the solution \( x < 4 \)
- \( 3.7x > 14.8 \) gives the solution \( x > 4 \)
- \( 2.8x < 10.5 \) gives the solution \( x < 3.75 \)

If Paolo's graph indicates a solution greater than \( 4 \), then the inequalities he solved would be either \( 4.9x > 19.6 \) or \( 3.7x > 14.8 \).

If the graph shows a solution less than \( 4 \), it could be \( 2.1x < 8.4 \) or \( 2.8x < 10.5 \); specifically, the latter would be less than \( 3.75 \).

From the options available, without the graph itself, we cannot definitively determine which inequality Paolo solved, but based on logical deductions:

- If the graph shows values greater than 4, Paolo solved either \( 4.9x > 19.6 \) or \( 3.7x > 14.8 \).
- If the graph shows values less than 4, he solved either \( 2.1x < 8.4 \) or \( 2.8x < 10.5\).

To accurately answer, we would need to know the type of solutions indicated on the graph. If you have that information, please provide it.