Question

Paolo solved an inequality and graphed the solution on the number line. Which of the following inequalities did he solve?

(1 point)

A. 3.7x>14.8

B. 2.8x<10.5

C. 2.1x<8.4

D. 4.9x>19.6

Answer 1

To determine which inequality Paolo solved, we need to solve each inequality for \( x \) and see what intervals would be represented on a number line.

**A.**
\( 3.7x > 14.8 \)

Dividing both sides by 3.7:
\[
x > \frac{14.8}{3.7} \approx 4
\]

**B.**
\( 2.8x < 10.5 \)

Dividing both sides by 2.8:
\[
x < \frac{10.5}{2.8} \approx 3.75
\]

**C.**
\( 2.1x < 8.4 \)

Dividing both sides by 2.1:
\[
x < \frac{8.4}{2.1} = 4
\]

**D.**
\( 4.9x > 19.6 \)

Dividing both sides by 4.9:
\[
x > \frac{19.6}{4.9} = 4
\]

Now we can summarize the solutions:
- A: \( x > 4 \) (open interval to the right of 4)
- B: \( x < 3.75 \) (open interval to the left of 3.75)
- C: \( x < 4 \) (open interval to the left of 4)
- D: \( x > 4 \) (same as A, open interval to the right of 4)

Without knowing the exact representation of the graph on the number line, it seems that both options A and D give the same solution of \( x > 4 \), while options B and C reflect values less than 4.

If the graphed solution was an open interval that extends to the right of 4, then the correct answers would be either A or D based on how they are commonly expressed.

If I had to give a definitive answer based on this information, it would be:
### A. \( 3.7x > 14.8 \) or D. \( 4.9x > 19.6 \) (both yield \( x > 4 \)).