Question

Use the image to answer the 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

2.8x<10.5
2.8 x less than 10.5

2.1x<8.4
2.1 x less than 8.4

3.7x>14.8
3.7 x greater than 14.8

4.9x>19.6

Answer 1

To determine which inequality Paolo solved, we can analyze the details given about the number line. The number line has an open circle at 4, with a leftward arrow indicating that the solution includes all values less than 4 (but not including 4 itself).

Hence, the correct inequality is of the form \( x < 4 \).

Now, let’s examine the options given:

1. **2.8x < 10.5**
To solve for x:
\( x < \frac{10.5}{2.8} \)
\( x < 3.75 \) (which does not support x < 4)

2. **2.1x < 8.4**
To solve for x:
\( x < \frac{8.4}{2.1} \)
\( x < 4 \) (this supports the solution)

3. **3.7x > 14.8**
To solve for x:
\( x > \frac{14.8}{3.7} \)
\( x > 4 \) (which is the opposite of our required solution)

4. **4.9x > 19.6**
To solve for x:
\( x > \frac{19.6}{4.9} \)
\( x > 4 \) (which again is the opposite)

Based on this analysis, Paolo solved the inequality \( 2.1x < 8.4 \).