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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

2.8x<10.5
2.8 x less than 10.5

4.9x>19.6
4.9 x greater than 19.6

2.1x<8.4

Answer 1

To determine the inequality that Paolo solved, we need to interpret the information provided about the number line.

The number line has an open point at 4, and there is a leftward arrow from that point, indicating that the solution includes all values less than 4. Therefore, the solution to the inequality would be x < 4.

Now, we can analyze the given options:

1. \(3.7x > 14.8\) implies \(x > \frac{14.8}{3.7} \approx 4\) (not the correct direction).
2. \(2.8x < 10.5\) implies \(x < \frac{10.5}{2.8} \approx 3.75\) (this is less than 4).
3. \(4.9x > 19.6\) implies \(x > \frac{19.6}{4.9} = 4\) (not the correct direction).
4. \(2.1x < 8.4\) implies \(x < \frac{8.4}{2.1} = 4\) (this is also less than 4).

Since the solution must be values less than 4, both the second option \(2.8x < 10.5\) and the fourth option \(2.1x < 8.4\) are valid inequalities based on the information provided about the number line.

However, since the number line depicts values less than 4 and does not include 4, Paolo must have solved an inequality representing all numbers less than a value (not including that value), so the best fit would be the one with a solution that does not include the number 4.

Both options (2) and (4) satisfy \(x < 4\), but \(2.8x < 10.5\) gives a more restrictive condition as it gives a value less than 4.

Thus, the correct answer is:

2.8x < 10.5