Use the image to answer the question.

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

4.9x>19.6
4.9 x greater than 19.6

2.1x<8.4
2.1 x less than 8.4

2.8x<10.5
2.8 x less than 10.5

3.7x>14.8

Answer 1

To determine which inequality Paolo solved based on the graph, we can analyze the information provided.

The graph shows an open point at 4 and a leftward arrow indicating that the solution includes all values less than 4 (as the arrow continues to extend left, towards negative infinity). This means that the inequality is of the form \(x < 4\).

Next, we can examine the response options to see which one, when solved for \(x\), would yield a solution compatible with \(x < 4\):

1. \(4.9x > 19.6\)

   • Dividing both sides by 4.9 gives: \(x > 4\). (Not a match)

2. \(2.1x < 8.4\)

   • Dividing both sides by 2.1 gives: \(x < 4\). (Match)

3. \(2.8x < 10.5\)

   • Dividing both sides by 2.8 gives: \(x < 3.75\). (This is narrower than \(x < 4\), but still valid)

4. \(3.7x > 14.8\)

   • Dividing both sides by 3.7 gives: \(x > 4\). (Not a match)

Among the options, options 2 and 3 contain inequalities that are less than 4 and are therefore valid. However, option 2 explicitly states \(x < 4\), which represents the graph accurately.

Thus, the correct answer is: 2.1x < 8.4.