Question
Which inequality is true when the value of nn is minus, 15−15?
Answer
Multiple Choice Answers
n, minus, 4, is greater than, minus, 10n−4>−10
minus, n, minus, 4, is less than, 10−n−4<10
minus, n, minus, 4, is less than, minus, 10−n−4<−10
minus, n, minus, 4, is greater than, 10−n−4>10
Answer
Multiple Choice Answers
n, minus, 4, is greater than, minus, 10n−4>−10
minus, n, minus, 4, is less than, 10−n−4<10
minus, n, minus, 4, is less than, minus, 10−n−4<−10
minus, n, minus, 4, is greater than, 10−n−4>10
Answers
Answer
Solve the inequality and graph the solution on the line provided.
9, plus, 4, x, is greater than or equal to, 37
9+4x≥
37
Answer
Attempt 1 out of 2
Inequality Notation:
Number Line:
9, plus, 4, x, is greater than or equal to, 37
9+4x≥
37
Answer
Attempt 1 out of 2
Inequality Notation:
Number Line:
Answer
Solve the inequality and graph the solution on the line provided.
8, plus, 3, x, is greater than, 23
8+3x>
23
Answer
Attempt 1 out of 2
Inequality Notation:
Number Line:
Click and drag to plot line.
8, plus, 3, x, is greater than, 23
8+3x>
23
Answer
Attempt 1 out of 2
Inequality Notation:
Number Line:
Click and drag to plot line.
Answer
Solve the inequality and graph the solution on the line provided.
5, x, plus, 54, is greater than or equal to, 74
5x+54≥
74
Answer
Attempt 1 out of 2
Inequality Notation:
Number Line:
5, x, plus, 54, is greater than or equal to, 74
5x+54≥
74
Answer
Attempt 1 out of 2
Inequality Notation:
Number Line:
Answered by
GPT-4o mini
To evaluate the inequalities given the condition \( n = -15 \), we will substitute \( n \) into each inequality and see which one holds true.
1. **First Inequality**:
\[
-n - 4 > -10
\]
Substituting \( n = -15 \):
\[
-(-15) - 4 > -10 \implies 15 - 4 > -10 \implies 11 > -10 \quad \text{(True)}
\]
2. **Second Inequality**:
\[
-n - 4 < 10
\]
Substituting \( n = -15 \):
\[
-(-15) - 4 < 10 \implies 15 - 4 < 10 \implies 11 < 10 \quad \text{(False)}
\]
3. **Third Inequality**:
\[
-n - 4 < -10
\]
Substituting \( n = -15 \):
\[
-(-15) - 4 < -10 \implies 15 - 4 < -10 \implies 11 < -10 \quad \text{(False)}
\]
4. **Fourth Inequality**:
\[
-n - 4 > 10
\]
Substituting \( n = -15 \):
\[
-(-15) - 4 > 10 \implies 15 - 4 > 10 \implies 11 > 10 \quad \text{(True)}
\]
So, we have:
- The first inequality is true.
- The second inequality is false.
- The third inequality is false.
- The fourth inequality is true.
Thus, both the first and the fourth inequalities are true when \( n = -15 \). However, since we are only to select one option, the **first inequality**:
\[
-n - 4 > -10
\]
is a valid answer.
The answer from the multiple choices that is true is:
- \( -n - 4 > -10 \)
1. **First Inequality**:
\[
-n - 4 > -10
\]
Substituting \( n = -15 \):
\[
-(-15) - 4 > -10 \implies 15 - 4 > -10 \implies 11 > -10 \quad \text{(True)}
\]
2. **Second Inequality**:
\[
-n - 4 < 10
\]
Substituting \( n = -15 \):
\[
-(-15) - 4 < 10 \implies 15 - 4 < 10 \implies 11 < 10 \quad \text{(False)}
\]
3. **Third Inequality**:
\[
-n - 4 < -10
\]
Substituting \( n = -15 \):
\[
-(-15) - 4 < -10 \implies 15 - 4 < -10 \implies 11 < -10 \quad \text{(False)}
\]
4. **Fourth Inequality**:
\[
-n - 4 > 10
\]
Substituting \( n = -15 \):
\[
-(-15) - 4 > 10 \implies 15 - 4 > 10 \implies 11 > 10 \quad \text{(True)}
\]
So, we have:
- The first inequality is true.
- The second inequality is false.
- The third inequality is false.
- The fourth inequality is true.
Thus, both the first and the fourth inequalities are true when \( n = -15 \). However, since we are only to select one option, the **first inequality**:
\[
-n - 4 > -10
\]
is a valid answer.
The answer from the multiple choices that is true is:
- \( -n - 4 > -10 \)
Answered by
GPT-4o mini
To solve the inequality \( 9 + 4x \geq 37 \), we will isolate \( x \).
### Steps to solve:
1. **Subtract 9 from both sides**:
\[
4x \geq 37 - 9
\]
\[
4x \geq 28
\]
2. **Divide by 4**:
\[
x \geq \frac{28}{4}
\]
\[
x \geq 7
\]
### Solution in inequality notation:
The solution to the inequality is:
\[
x \geq 7
\]
### Graphing the solution on a number line:
- Draw a number line.
- Place a closed circle (or dot) at \( 7 \) since the inequality includes the equal to sign (≥).
- Shade the line to the right of \( 7 \) to indicate that the solution includes all numbers greater than or equal to \( 7 \).
### Summary:
- **Inequality Notation**: \( x \geq 7 \)
- **Number Line**:
- Use a closed circle at \( 7 \) and shade to the right.
If you need a visual representation, imagine the following:
```
<---|---|---|---|---|---|---|---|---|---|---|---
4 5 6 (7)========================>
```
The closed circle at 7 indicates that \( 7 \) is included in the solution set. The arrow extending to the right indicates all values greater than \( 7 \) are included.
### Steps to solve:
1. **Subtract 9 from both sides**:
\[
4x \geq 37 - 9
\]
\[
4x \geq 28
\]
2. **Divide by 4**:
\[
x \geq \frac{28}{4}
\]
\[
x \geq 7
\]
### Solution in inequality notation:
The solution to the inequality is:
\[
x \geq 7
\]
### Graphing the solution on a number line:
- Draw a number line.
- Place a closed circle (or dot) at \( 7 \) since the inequality includes the equal to sign (≥).
- Shade the line to the right of \( 7 \) to indicate that the solution includes all numbers greater than or equal to \( 7 \).
### Summary:
- **Inequality Notation**: \( x \geq 7 \)
- **Number Line**:
- Use a closed circle at \( 7 \) and shade to the right.
If you need a visual representation, imagine the following:
```
<---|---|---|---|---|---|---|---|---|---|---|---
4 5 6 (7)========================>
```
The closed circle at 7 indicates that \( 7 \) is included in the solution set. The arrow extending to the right indicates all values greater than \( 7 \) are included.
Answered by
GPT-4o mini
To solve the inequality \( 8 + 3x > 23 \), let’s follow the steps to isolate \( x \).
### Steps to Solve the Inequality:
1. **Subtract 8 from both sides**:
\[
3x > 23 - 8
\]
\[
3x > 15
\]
2. **Divide by 3**:
\[
x > \frac{15}{3}
\]
\[
x > 5
\]
### Solution in Inequality Notation:
The solution to the inequality is:
\[
x > 5
\]
### Graphing the Solution on a Number Line:
1. Draw a number line.
2. Place an **open circle** at \( 5 \) because the inequality does not include \( 5 \) (it is strictly greater).
3. Shade the line to the right of \( 5 \) to indicate that all numbers greater than \( 5 \) are included in the solution.
### Summary:
- **Inequality Notation**: \( x > 5 \)
- **Number Line**:
- Use an open circle at \( 5 \) and shade to the right.
If you need to visualize it:
```
<---|---|---|---|---|---|---|---|---|---|---|---
2 3 4 (5)========================>
```
This representation shows an open circle at \( 5 \) with shading extending to the right, indicating that all values greater than \( 5 \) are part of the solution.
Feel free to click and drag to plot the line as needed!
### Steps to Solve the Inequality:
1. **Subtract 8 from both sides**:
\[
3x > 23 - 8
\]
\[
3x > 15
\]
2. **Divide by 3**:
\[
x > \frac{15}{3}
\]
\[
x > 5
\]
### Solution in Inequality Notation:
The solution to the inequality is:
\[
x > 5
\]
### Graphing the Solution on a Number Line:
1. Draw a number line.
2. Place an **open circle** at \( 5 \) because the inequality does not include \( 5 \) (it is strictly greater).
3. Shade the line to the right of \( 5 \) to indicate that all numbers greater than \( 5 \) are included in the solution.
### Summary:
- **Inequality Notation**: \( x > 5 \)
- **Number Line**:
- Use an open circle at \( 5 \) and shade to the right.
If you need to visualize it:
```
<---|---|---|---|---|---|---|---|---|---|---|---
2 3 4 (5)========================>
```
This representation shows an open circle at \( 5 \) with shading extending to the right, indicating that all values greater than \( 5 \) are part of the solution.
Feel free to click and drag to plot the line as needed!
Answered by
GPT-4o mini
To solve the inequality \( 5x + 54 \geq 74 \), let's follow the steps to isolate \( x \).
### Steps to Solve the Inequality:
1. **Subtract 54 from both sides**:
\[
5x \geq 74 - 54
\]
\[
5x \geq 20
\]
2. **Divide by 5**:
\[
x \geq \frac{20}{5}
\]
\[
x \geq 4
\]
### Solution in Inequality Notation:
The solution to the inequality is:
\[
x \geq 4
\]
### Graphing the Solution on a Number Line:
1. Draw a number line.
2. Place a **closed circle** at \( 4 \) because the inequality includes \( 4 \) (it is "greater than or equal to").
3. Shade the line to the right of \( 4 \) to indicate that all numbers greater than or equal to \( 4 \) are included in the solution.
### Summary:
- **Inequality Notation**: \( x \geq 4 \)
- **Number Line**:
- Use a closed circle at \( 4 \) and shade to the right.
If you were to visualize this:
```
<---|---|---|---|---|---|---|---|---|---|---|---
1 2 3 (4)========================>
```
This representation shows a closed circle at \( 4 \) with shading extending to the right, indicating that all values \( 4 \) and greater are part of the solution.
You can now drag and plot this on your provided number line!
### Steps to Solve the Inequality:
1. **Subtract 54 from both sides**:
\[
5x \geq 74 - 54
\]
\[
5x \geq 20
\]
2. **Divide by 5**:
\[
x \geq \frac{20}{5}
\]
\[
x \geq 4
\]
### Solution in Inequality Notation:
The solution to the inequality is:
\[
x \geq 4
\]
### Graphing the Solution on a Number Line:
1. Draw a number line.
2. Place a **closed circle** at \( 4 \) because the inequality includes \( 4 \) (it is "greater than or equal to").
3. Shade the line to the right of \( 4 \) to indicate that all numbers greater than or equal to \( 4 \) are included in the solution.
### Summary:
- **Inequality Notation**: \( x \geq 4 \)
- **Number Line**:
- Use a closed circle at \( 4 \) and shade to the right.
If you were to visualize this:
```
<---|---|---|---|---|---|---|---|---|---|---|---
1 2 3 (4)========================>
```
This representation shows a closed circle at \( 4 \) with shading extending to the right, indicating that all values \( 4 \) and greater are part of the solution.
You can now drag and plot this on your provided number line!
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