Question
Kayla created the graph below to represent the solution to the inequality x<−3
. What two errors did Kayla make?
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
(-3-10)
(2 points)
Responses
She should have used a closed circle at the end of the ray.
She should have used a closed circle at the end of the ray.
She should have used a circle at –4 as the end of the ray.
She should have used a circle at –4 as the end of the ray.
She should have used a circle at –2 as the end of the ray.
She should have used a circle at –2 as the end of the ray.
She should have pointed the arrow to the left.
. What two errors did Kayla make?
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
(-3-10)
(2 points)
Responses
She should have used a closed circle at the end of the ray.
She should have used a closed circle at the end of the ray.
She should have used a circle at –4 as the end of the ray.
She should have used a circle at –4 as the end of the ray.
She should have used a circle at –2 as the end of the ray.
She should have used a circle at –2 as the end of the ray.
She should have pointed the arrow to the left.
Answers
Answered by
GPT-4o mini
To analyze the errors Kayla made in representing the inequality \( x < -3 \):
1. The correct representation of the inequality \( x < -3 \) should use an **open circle** at -3 because the inequality is strictly less than (not less than or equal to). If Kayla used a closed circle, this would be incorrect.
2. The arrow should point left because the inequality indicates all numbers less than -3, which is to the left on a number line.
Based on these two points of analysis, the errors Kayla made are:
1. **She should have used an open circle at -3 instead of a closed circle.**
2. **She should have pointed the arrow to the left.**
Among the responses provided:
- **She should have used a closed circle at the end of the ray.** (Incorrect)
- **She should have used a circle at –4 as the end of the ray.** (Incorrect)
- **She should have used a circle at –2 as the end of the ray.** (Incorrect)
- **She should have pointed the arrow to the left.** (Correct)
Thus, her errors were not correctly represented in the response choices, but you can conclude that she should use an open circle at -3 (not mentioned), and the arrow should correctly point left.
1. The correct representation of the inequality \( x < -3 \) should use an **open circle** at -3 because the inequality is strictly less than (not less than or equal to). If Kayla used a closed circle, this would be incorrect.
2. The arrow should point left because the inequality indicates all numbers less than -3, which is to the left on a number line.
Based on these two points of analysis, the errors Kayla made are:
1. **She should have used an open circle at -3 instead of a closed circle.**
2. **She should have pointed the arrow to the left.**
Among the responses provided:
- **She should have used a closed circle at the end of the ray.** (Incorrect)
- **She should have used a circle at –4 as the end of the ray.** (Incorrect)
- **She should have used a circle at –2 as the end of the ray.** (Incorrect)
- **She should have pointed the arrow to the left.** (Correct)
Thus, her errors were not correctly represented in the response choices, but you can conclude that she should use an open circle at -3 (not mentioned), and the arrow should correctly point left.