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

3.7x>14.8
3.7 x greater than 14.8

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

Answer 1

2.8x<10.5

Explanation: Based on the image, an open point is plotted on the number line at 4, and a leftward arrow is marked from that point beyond negative 10. This indicates that the variable x must be less than 4 and greater than or equal to negative 10. The only inequality that fits this description is 2.8x<10.5.

Answer 2

Question
Solve 8x−14≤10 . Make sure to write your inequality so that x comes first.(1 point)

Answer 3

To solve the inequality 8x - 14 ≤ 10, we can follow these steps:

1. Add 14 to both sides of the inequality: 8x - 14 + 14 ≤ 10 + 14
This simplifies to: 8x ≤ 24

2. Divide both sides of the inequality by 8: (8x)/8 ≤ 24/8
This simplifies to: x ≤ 3

Therefore, the solution to the inequality is x ≤ 3.

Answer 4

Solve 5.14x+2.25>15.1 . Write the rational number in your answer in decimal form to the tenths place. Make sure to write your inequality so that x comes first.(1 point)

Answer 5

To solve the inequality 5.14x + 2.25 > 15.1, we can follow these steps:

1. Subtract 2.25 from both sides of the inequality: 5.14x + 2.25 - 2.25 > 15.1 - 2.25
This simplifies to: 5.14x > 12.85

2. Divide both sides of the inequality by 5.14: (5.14x)/5.14 > 12.85/5.14
This simplifies to: x > 2.5

Therefore, the solution to the inequality is x > 2.5.