Question
Kayla created the graph below to represent the solution to the inequality −8<x
. What two errors did Kayla make?
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(2 points)
Responses
She should have used a circle at –9 as the end of the ray.
She should have used a circle at –9 as the end of the ray.
She should have used a circle at –7 as the end of the ray.
She should have used a circle at –7 as the end of the ray.
She should have used an open circle at the end of the ray.
She should have used an open circle at the end of the ray.
She should have pointed the arrow to the right.
. What two errors did Kayla make?
NOTE: There is a check answer button in the bottom right corner. Click this to check your answer before moving on to the next question. It will not tell you the correct answer, but it will tell you if the answer you selected is correct. You can use this feature once per question.
(2 points)
Responses
She should have used a circle at –9 as the end of the ray.
She should have used a circle at –9 as the end of the ray.
She should have used a circle at –7 as the end of the ray.
She should have used a circle at –7 as the end of the ray.
She should have used an open circle at the end of the ray.
She should have used an open circle at the end of the ray.
She should have pointed the arrow to the right.
Answers
Answered by
GPT-4o mini
To analyze Kayla's graph of the inequality \( -8 < x \), we can identify the errors based on the properties of inequalities.
1. The inequality \( -8 < x \) indicates that \( x \) is greater than \(-8\). This means that we should not include \(-8\) itself in the solution set, which requires using an open circle at \(-8\). Specifically, this means she should have used an open circle at the end of the ray, indicating that \(-8\) is not included.
2. Since the inequality is \( x > -8\), the graph should represent all numbers greater than \(-8\), which means the arrow should point to the right, towards positive infinity. If she pointed the arrow in the opposite direction, that would be a mistake.
Based on these explanations, the two errors Kayla made are:
- **She should have used an open circle at the end of the ray.**
- **She should have pointed the arrow to the right.**
These options align with the correct approach to graphing the inequality \( -8 < x \).
1. The inequality \( -8 < x \) indicates that \( x \) is greater than \(-8\). This means that we should not include \(-8\) itself in the solution set, which requires using an open circle at \(-8\). Specifically, this means she should have used an open circle at the end of the ray, indicating that \(-8\) is not included.
2. Since the inequality is \( x > -8\), the graph should represent all numbers greater than \(-8\), which means the arrow should point to the right, towards positive infinity. If she pointed the arrow in the opposite direction, that would be a mistake.
Based on these explanations, the two errors Kayla made are:
- **She should have used an open circle at the end of the ray.**
- **She should have pointed the arrow to the right.**
These options align with the correct approach to graphing the inequality \( -8 < x \).
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