Question
Interpret and graph the inequality.
x less or equal than negative 3 space o r space x greater than 7
Be sure to choose a whole number to the left and to the right as your test point. Then use the correct one to create the second point of the ray to show the shading of the number line for the solution set.
Click on the circle and turn to white if wanting to show an open circle.
Answer:
Write an optional reasoning for your answer:
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Question 2
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Interpret and graph the inequality.
negative 12 less than x less or equal than 9
Answer:
Write an optional reasoning for your answer:
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Question 3
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Interpret and graph the inequality.
x less or equal than negative 1.5 space o r space x greater than 5
Be sure to choose a whole number to the left and to the right as your test point. Then use the correct one to create the second point of the ray to show the shading of the number line for the solution set.
Click on the circle and turn to white if wanting to show an open circle.
Answer:
Write an optional reasoning for your answer:
Answer text Question 3
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Question 4
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Interpret and graph the inequality.
x greater or equal than negative 2 space a n d space x less than 5
Answer:
Write an optional reasoning for your answer:
Answer text Question 4
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x less or equal than negative 3 space o r space x greater than 7
Be sure to choose a whole number to the left and to the right as your test point. Then use the correct one to create the second point of the ray to show the shading of the number line for the solution set.
Click on the circle and turn to white if wanting to show an open circle.
Answer:
Write an optional reasoning for your answer:
Answer text Question 1
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Question 2
Tries remaining: 3
Marked out of 1.00
Question text
Interpret and graph the inequality.
negative 12 less than x less or equal than 9
Answer:
Write an optional reasoning for your answer:
Answer text Question 2
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Question 3
Tries remaining: 3
Marked out of 1.00
Question text
Interpret and graph the inequality.
x less or equal than negative 1.5 space o r space x greater than 5
Be sure to choose a whole number to the left and to the right as your test point. Then use the correct one to create the second point of the ray to show the shading of the number line for the solution set.
Click on the circle and turn to white if wanting to show an open circle.
Answer:
Write an optional reasoning for your answer:
Answer text Question 3
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Question 4
Tries remaining: 3
Marked out of 1.00
Question text
Interpret and graph the inequality.
x greater or equal than negative 2 space a n d space x less than 5
Answer:
Write an optional reasoning for your answer:
Answer text Question 4
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Answers
GPT-4o mini
Here are the interpretations and graphs of the provided inequalities:
### Question 1:
**Inequality:** \( x \leq -3 \) or \( x > 7 \)
1. **Interpretation:**
- The solution set includes all numbers less than or equal to -3 and all numbers greater than 7.
2. **Test Points:**
- Choose \( x = -4 \) (left of -3) and \( x = 8 \) (right of 7).
- For \( x = -4 \): \(-4 \leq -3\) is true.
- For \( x = 8 \): \(8 > 7\) is true.
Both test points confirm the inequalities are satisfied in their respective intervals.
3. **Graph:**
- Draw an open circle at -3 (to indicate it is included) and shade leftwards.
- Draw an open circle at 7 (to indicate it is not included) and shade rightwards.
### Answer:
**Graph:**
- \[\text{-3 (closed circle)}\] (all numbers left of -3)
- \[\text{7 (open circle)}\] (all numbers right of 7)
**Reasoning:**
The boundaries indicate where the values change from one inequality being valid to the other. The solution includes all values less than or equal to -3 and all values greater than 7.
---
### Question 2:
**Inequality:** \( -12 < x \leq 9 \)
1. **Interpretation:**
- The solution set includes all numbers greater than -12 and all numbers less than or equal to 9.
2. **Test Points:**
- Choose \( x = -11 \) (right of -12) and \( x = 10 \) (right of 9).
- For \( x = -11 \): \(-11 > -12\) is true.
- For \( x = 10 \): \(10 \leq 9\) is false.
Thus, -11 is valid and 10 is not.
3. **Graph:**
- Draw an open circle at -12 (not included) and shade rightwards.
- Draw a closed circle at 9 (included) and shade leftwards.
### Answer:
**Graph:**
- \( -12 \text{ (open circle)} \) (all numbers strictly more than -12)
- \( 9 \text{ (closed circle)} \) (all numbers less than or equal to 9)
**Reasoning:**
The inequality defines a range where values start just above -12 and include all values up to and including 9.
---
### Question 3:
**Inequality:** \( x \leq -1.5 \) or \( x > 5 \)
1. **Interpretation:**
- The solution set includes all numbers less than or equal to -1.5 and all numbers greater than 5.
2. **Test Points:**
- Choose \( x = -2 \) (left of -1.5) and \( x = 6 \) (right of 5).
- For \( x = -2 \): \(-2 \leq -1.5\) is true.
- For \( x = 6 \): \(6 > 5\) is true.
Both test points confirm the inequalities are satisfied in their respective intervals.
3. **Graph:**
- Draw a closed circle at -1.5 (to indicate it is included) and shade leftwards.
- Draw an open circle at 5 (not included) and shade rightwards.
### Answer:
**Graph:**
- \[-1.5 \text{ (closed circle)}\] (all numbers left of -1.5)
- \[5 \text{ (open circle)}\] (all numbers right of 5)
**Reasoning:**
The solution contains values that encompass everything less than or equal to -1.5 and everything greater than 5.
---
### Question 4:
**Inequality:** \( x \geq -2 \) and \( x < 5 \)
1. **Interpretation:**
- The solution set includes all numbers greater than or equal to -2 and less than 5.
2. **Test Points:**
- Choose \( x = -1 \) (valid point) and \( x = 6 \) (outside range).
- For \( x = -1 \): \(-1 \geq -2\) is true and \(-1 < 5\) is true.
- For \( x = 6 \): \(6 < 5\) is false.
Thus, -1 is valid and 6 is not.
3. **Graph:**
- Draw a closed circle at -2 (included) and shade rightwards.
- Draw an open circle at 5 (not included) and shade leftwards.
### Answer:
**Graph:**
- \[-2 \text{ (closed circle)}\] (all numbers starting from -2)
- \[5 \text{ (open circle)}\] (all numbers up to but not including 5)
**Reasoning:**
This defines a closed interval from -2 to 5, showing that we include -2 but do not include 5.
### Question 1:
**Inequality:** \( x \leq -3 \) or \( x > 7 \)
1. **Interpretation:**
- The solution set includes all numbers less than or equal to -3 and all numbers greater than 7.
2. **Test Points:**
- Choose \( x = -4 \) (left of -3) and \( x = 8 \) (right of 7).
- For \( x = -4 \): \(-4 \leq -3\) is true.
- For \( x = 8 \): \(8 > 7\) is true.
Both test points confirm the inequalities are satisfied in their respective intervals.
3. **Graph:**
- Draw an open circle at -3 (to indicate it is included) and shade leftwards.
- Draw an open circle at 7 (to indicate it is not included) and shade rightwards.
### Answer:
**Graph:**
- \[\text{-3 (closed circle)}\] (all numbers left of -3)
- \[\text{7 (open circle)}\] (all numbers right of 7)
**Reasoning:**
The boundaries indicate where the values change from one inequality being valid to the other. The solution includes all values less than or equal to -3 and all values greater than 7.
---
### Question 2:
**Inequality:** \( -12 < x \leq 9 \)
1. **Interpretation:**
- The solution set includes all numbers greater than -12 and all numbers less than or equal to 9.
2. **Test Points:**
- Choose \( x = -11 \) (right of -12) and \( x = 10 \) (right of 9).
- For \( x = -11 \): \(-11 > -12\) is true.
- For \( x = 10 \): \(10 \leq 9\) is false.
Thus, -11 is valid and 10 is not.
3. **Graph:**
- Draw an open circle at -12 (not included) and shade rightwards.
- Draw a closed circle at 9 (included) and shade leftwards.
### Answer:
**Graph:**
- \( -12 \text{ (open circle)} \) (all numbers strictly more than -12)
- \( 9 \text{ (closed circle)} \) (all numbers less than or equal to 9)
**Reasoning:**
The inequality defines a range where values start just above -12 and include all values up to and including 9.
---
### Question 3:
**Inequality:** \( x \leq -1.5 \) or \( x > 5 \)
1. **Interpretation:**
- The solution set includes all numbers less than or equal to -1.5 and all numbers greater than 5.
2. **Test Points:**
- Choose \( x = -2 \) (left of -1.5) and \( x = 6 \) (right of 5).
- For \( x = -2 \): \(-2 \leq -1.5\) is true.
- For \( x = 6 \): \(6 > 5\) is true.
Both test points confirm the inequalities are satisfied in their respective intervals.
3. **Graph:**
- Draw a closed circle at -1.5 (to indicate it is included) and shade leftwards.
- Draw an open circle at 5 (not included) and shade rightwards.
### Answer:
**Graph:**
- \[-1.5 \text{ (closed circle)}\] (all numbers left of -1.5)
- \[5 \text{ (open circle)}\] (all numbers right of 5)
**Reasoning:**
The solution contains values that encompass everything less than or equal to -1.5 and everything greater than 5.
---
### Question 4:
**Inequality:** \( x \geq -2 \) and \( x < 5 \)
1. **Interpretation:**
- The solution set includes all numbers greater than or equal to -2 and less than 5.
2. **Test Points:**
- Choose \( x = -1 \) (valid point) and \( x = 6 \) (outside range).
- For \( x = -1 \): \(-1 \geq -2\) is true and \(-1 < 5\) is true.
- For \( x = 6 \): \(6 < 5\) is false.
Thus, -1 is valid and 6 is not.
3. **Graph:**
- Draw a closed circle at -2 (included) and shade rightwards.
- Draw an open circle at 5 (not included) and shade leftwards.
### Answer:
**Graph:**
- \[-2 \text{ (closed circle)}\] (all numbers starting from -2)
- \[5 \text{ (open circle)}\] (all numbers up to but not including 5)
**Reasoning:**
This defines a closed interval from -2 to 5, showing that we include -2 but do not include 5.