Question
Which inequality is true when the value of xx is 1818?
Answer
Multiple Choice Answers
minus, x, minus, 2, point, 5, is greater than, minus, 3−x−2.5>−3
minus, x, minus, 2, point, 5, is greater than, 3−x−2.5>3
x, minus, 2, point, 5, is less than, 3x−2.5<3
minus, x, minus, 2, point, 5, is less than, 3−x−2.5<3
Answer
Multiple Choice Answers
minus, x, minus, 2, point, 5, is greater than, minus, 3−x−2.5>−3
minus, x, minus, 2, point, 5, is greater than, 3−x−2.5>3
x, minus, 2, point, 5, is less than, 3x−2.5<3
minus, x, minus, 2, point, 5, is less than, 3−x−2.5<3
Answers
Answer
Solve the inequality and graph the solution on the line provided.
13, plus, 2, x, is greater than, minus, 3
13+2x>
−3
Answer
Attempt 1 out of 2
Inequality Notation:
Number Line:
13, plus, 2, x, is greater than, minus, 3
13+2x>
−3
Answer
Attempt 1 out of 2
Inequality Notation:
Number Line:
Answer
Solve the following inequality for ww. Write your answer in simplest form.
8, w, minus, 9, is greater than or equal to, w, minus, 7
8w−9≥
w−7
Answer
Attempt 1 out of 2
ww
8, w, minus, 9, is greater than or equal to, w, minus, 7
8w−9≥
w−7
Answer
Attempt 1 out of 2
ww
Answer
Solve for xx and graph the solution on the number line below.
4, x, plus, 8, is greater than or equal to, minus, 32, and, 48, is greater than, 4, x, plus, 8
4x+8≥−32and
48>4x+8
Answer
Attempt 1 out of 2
Inequality Notation:
Number Line:
4, x, plus, 8, is greater than or equal to, minus, 32, and, 48, is greater than, 4, x, plus, 8
4x+8≥−32and
48>4x+8
Answer
Attempt 1 out of 2
Inequality Notation:
Number Line:
Answer
Solve for xx and graph the solution on the number line below.
minus, x, minus, 3, is greater than or equal to, minus, 2, or, minus, x, minus, 3, is less than or equal to, minus, 9
−x−3≥−2or
−x−3≤−9
Answer
Attempt 1 out of 2
Inequality Notation:
Number Line:
minus, x, minus, 3, is greater than or equal to, minus, 2, or, minus, x, minus, 3, is less than or equal to, minus, 9
−x−3≥−2or
−x−3≤−9
Answer
Attempt 1 out of 2
Inequality Notation:
Number Line:
Answer
sm is rong
Answered by
GPT-4o mini
To determine which inequality is true when \(x = 18\), we can analyze each of the provided inequalities one by one.
1. **Inequality**: \(-x - 2.5 > -3\)
Substitute \(x = 18\):
\[
-18 - 2.5 > -3 \implies -20.5 > -3 \quad (\text{False})
\]
2. **Inequality**: \(-x - 2.5 > 3\)
Substitute \(x = 18\):
\[
-18 - 2.5 > 3 \implies -20.5 > 3 \quad (\text{False})
\]
3. **Inequality**: \(x - 2.5 < 3\)
Substitute \(x = 18\):
\[
18 - 2.5 < 3 \implies 15.5 < 3 \quad (\text{False})
\]
4. **Inequality**: \(-x - 2.5 < 3\)
Substitute \(x = 18\):
\[
-18 - 2.5 < 3 \implies -20.5 < 3 \quad (\text{True})
\]
After evaluating all the inequalities, the true statement when \(x = 18\) is:
\[
-x - 2.5 < 3
\]
Thus, the correct answer is:
**\(-x - 2.5 < 3\)**
1. **Inequality**: \(-x - 2.5 > -3\)
Substitute \(x = 18\):
\[
-18 - 2.5 > -3 \implies -20.5 > -3 \quad (\text{False})
\]
2. **Inequality**: \(-x - 2.5 > 3\)
Substitute \(x = 18\):
\[
-18 - 2.5 > 3 \implies -20.5 > 3 \quad (\text{False})
\]
3. **Inequality**: \(x - 2.5 < 3\)
Substitute \(x = 18\):
\[
18 - 2.5 < 3 \implies 15.5 < 3 \quad (\text{False})
\]
4. **Inequality**: \(-x - 2.5 < 3\)
Substitute \(x = 18\):
\[
-18 - 2.5 < 3 \implies -20.5 < 3 \quad (\text{True})
\]
After evaluating all the inequalities, the true statement when \(x = 18\) is:
\[
-x - 2.5 < 3
\]
Thus, the correct answer is:
**\(-x - 2.5 < 3\)**
Answered by
GPT-4o mini
To solve the inequality \( 13 + 2x > -3 \), follow these steps:
1. **Isolate the term with \( x \)**:
\[
2x > -3 - 13
\]
\[
2x > -16
\]
2. **Divide both sides by 2**:
\[
x > -8
\]
### Inequality Notation:
The solution in inequality notation is:
\[
x > -8
\]
### Graphing the Solution:
To graph this solution on a number line:
- Draw a number line.
- Mark the point -8.
- Since it is a strict inequality (greater than), use an open circle at -8 to indicate that -8 is not included in the solution.
- Shade the line to the right of -8 to represent all values greater than -8.
Here is a textual representation of the number line:
```
<-----O=======>
-8
```
In this representation:
- The "O" at -8 is an open circle.
- The "=" sign indicates that the line extends to the right (all numbers greater than -8).
This properly conveys that \( x \) can take any value greater than -8.
1. **Isolate the term with \( x \)**:
\[
2x > -3 - 13
\]
\[
2x > -16
\]
2. **Divide both sides by 2**:
\[
x > -8
\]
### Inequality Notation:
The solution in inequality notation is:
\[
x > -8
\]
### Graphing the Solution:
To graph this solution on a number line:
- Draw a number line.
- Mark the point -8.
- Since it is a strict inequality (greater than), use an open circle at -8 to indicate that -8 is not included in the solution.
- Shade the line to the right of -8 to represent all values greater than -8.
Here is a textual representation of the number line:
```
<-----O=======>
-8
```
In this representation:
- The "O" at -8 is an open circle.
- The "=" sign indicates that the line extends to the right (all numbers greater than -8).
This properly conveys that \( x \) can take any value greater than -8.
Answered by
GPT-4o mini
To solve the inequality \( 8w - 9 \geq w - 7 \), follow these steps:
1. **Move all terms involving \( w \) to one side of the inequality**. We can do this by subtracting \( w \) from both sides:
\[
8w - w - 9 \geq -7
\]
\[
7w - 9 \geq -7
\]
2. **Next, add 9 to both sides to isolate the term with \( w \)**:
\[
7w \geq -7 + 9
\]
\[
7w \geq 2
\]
3. **Finally, divide both sides by 7** to solve for \( w \):
\[
w \geq \frac{2}{7}
\]
### Final answer in simplest form:
The solution to the inequality in simplest form is:
\[
w \geq \frac{2}{7}
\]
1. **Move all terms involving \( w \) to one side of the inequality**. We can do this by subtracting \( w \) from both sides:
\[
8w - w - 9 \geq -7
\]
\[
7w - 9 \geq -7
\]
2. **Next, add 9 to both sides to isolate the term with \( w \)**:
\[
7w \geq -7 + 9
\]
\[
7w \geq 2
\]
3. **Finally, divide both sides by 7** to solve for \( w \):
\[
w \geq \frac{2}{7}
\]
### Final answer in simplest form:
The solution to the inequality in simplest form is:
\[
w \geq \frac{2}{7}
\]
Answered by
GPT-4o mini
To solve the compound inequalities:
1. **First Inequality**: \( 4x + 8 \geq -32 \)
- Subtract 8 from both sides:
\[
4x \geq -32 - 8
\]
\[
4x \geq -40
\]
- Divide both sides by 4:
\[
x \geq -10
\]
2. **Second Inequality**: \( 48 > 4x + 8 \)
- Subtract 8 from both sides:
\[
48 - 8 > 4x
\]
\[
40 > 4x
\]
- Divide both sides by 4:
\[
10 > x
\]
or
\[
x < 10
\]
### Combine the Results
The combined solution from the two inequalities is:
\[
-10 \leq x < 10
\]
### Inequality Notation:
In inequality notation, the solution can be expressed as:
\[
-10 \leq x < 10
\]
### Graphing the Solution:
To graph this solution on a number line:
1. Draw a number line.
2. Mark the points -10 and 10.
3. Use a closed circle at -10 (to include -10) and an open circle at 10 (since 10 is not included).
4. Shade the region between -10 and 10.
Here is a textual representation of the number line:
```
<===●================○===>
-10 10
```
In this representation:
- The "●" (filled circle) at -10 indicates that -10 is included in the solution.
- The "○" (open circle) at 10 indicates that 10 is not included in the solution.
- The shaded line represents all values between -10 and 10 (including -10 but not including 10).
1. **First Inequality**: \( 4x + 8 \geq -32 \)
- Subtract 8 from both sides:
\[
4x \geq -32 - 8
\]
\[
4x \geq -40
\]
- Divide both sides by 4:
\[
x \geq -10
\]
2. **Second Inequality**: \( 48 > 4x + 8 \)
- Subtract 8 from both sides:
\[
48 - 8 > 4x
\]
\[
40 > 4x
\]
- Divide both sides by 4:
\[
10 > x
\]
or
\[
x < 10
\]
### Combine the Results
The combined solution from the two inequalities is:
\[
-10 \leq x < 10
\]
### Inequality Notation:
In inequality notation, the solution can be expressed as:
\[
-10 \leq x < 10
\]
### Graphing the Solution:
To graph this solution on a number line:
1. Draw a number line.
2. Mark the points -10 and 10.
3. Use a closed circle at -10 (to include -10) and an open circle at 10 (since 10 is not included).
4. Shade the region between -10 and 10.
Here is a textual representation of the number line:
```
<===●================○===>
-10 10
```
In this representation:
- The "●" (filled circle) at -10 indicates that -10 is included in the solution.
- The "○" (open circle) at 10 indicates that 10 is not included in the solution.
- The shaded line represents all values between -10 and 10 (including -10 but not including 10).
Answered by
GPT-4o mini
Let's solve each inequality step by step:
### First Inequality:
\(-x - 3 \geq -2\)
1. **Add 3 to both sides**:
\[
-x \geq -2 + 3
\]
\[
-x \geq 1
\]
2. **Multiply by -1** (remember to reverse the inequality sign):
\[
x \leq -1
\]
### Second Inequality:
\(-x - 3 \leq -9\)
1. **Add 3 to both sides**:
\[
-x \leq -9 + 3
\]
\[
-x \leq -6
\]
2. **Multiply by -1** (again, reverse the inequality sign):
\[
x \geq 6
\]
### Combined Solution
The solutions are:
- From the first inequality: \( x \leq -1 \)
- From the second inequality: \( x \geq 6 \)
Since this is an "or" statement, both parts represent valid solutions.
### Inequality Notation:
In inequality notation, the solution is:
\[
x \leq -1 \quad \text{or} \quad x \geq 6
\]
### Graphing the Solution:
To graph this on a number line:
1. Draw a number line.
2. Mark the points -1 and 6.
3. Use a closed circle at -1 (to include -1) and another closed circle at 6 (to include 6).
4. Shade to the left of -1 and to the right of 6 to represent all values \(x \leq -1\) and \(x \geq 6\).
Here's a textual representation of the number line:
```
<===●========|=======●===>
-1 0 6
```
- The "●" (filled circle) at -1 indicates that -1 is included in the solution.
- The "●" (filled circle) at 6 indicates that 6 is included in the solution.
- The shaded line to the left of -1 indicates all values less than or equal to -1, and the shaded line to the right of 6 indicates all values greater than or equal to 6.
### First Inequality:
\(-x - 3 \geq -2\)
1. **Add 3 to both sides**:
\[
-x \geq -2 + 3
\]
\[
-x \geq 1
\]
2. **Multiply by -1** (remember to reverse the inequality sign):
\[
x \leq -1
\]
### Second Inequality:
\(-x - 3 \leq -9\)
1. **Add 3 to both sides**:
\[
-x \leq -9 + 3
\]
\[
-x \leq -6
\]
2. **Multiply by -1** (again, reverse the inequality sign):
\[
x \geq 6
\]
### Combined Solution
The solutions are:
- From the first inequality: \( x \leq -1 \)
- From the second inequality: \( x \geq 6 \)
Since this is an "or" statement, both parts represent valid solutions.
### Inequality Notation:
In inequality notation, the solution is:
\[
x \leq -1 \quad \text{or} \quad x \geq 6
\]
### Graphing the Solution:
To graph this on a number line:
1. Draw a number line.
2. Mark the points -1 and 6.
3. Use a closed circle at -1 (to include -1) and another closed circle at 6 (to include 6).
4. Shade to the left of -1 and to the right of 6 to represent all values \(x \leq -1\) and \(x \geq 6\).
Here's a textual representation of the number line:
```
<===●========|=======●===>
-1 0 6
```
- The "●" (filled circle) at -1 indicates that -1 is included in the solution.
- The "●" (filled circle) at 6 indicates that 6 is included in the solution.
- The shaded line to the left of -1 indicates all values less than or equal to -1, and the shaded line to the right of 6 indicates all values greater than or equal to 6.
Answered by
GPT-4o mini
I apologize for any confusion in my previous responses. Let's carefully resolve the inequalities step by step, ensuring correctness:
### Given Inequalities:
1. \(-x - 3 \geq -2\)
2. \(-x - 3 \leq -9\)
### Solve the First Inequality:
\(-x - 3 \geq -2\)
1. **Add 3 to both sides**:
\[
-x \geq -2 + 3
\]
\[
-x \geq 1
\]
2. **Multiply by -1** (remember to reverse the inequality sign):
\[
x \leq -1
\]
### Solve the Second Inequality:
\(-x - 3 \leq -9\)
1. **Add 3 to both sides**:
\[
-x \leq -9 + 3
\]
\[
-x \leq -6
\]
2. **Multiply by -1** (again, reverse the inequality sign):
\[
x \geq 6
\]
### Combined Solution:
From the results, we have:
- First inequality: \( x \leq -1 \)
- Second inequality: \( x \geq 6 \)
The solution can be expressed as:
\[
x \leq -1 \quad \text{or} \quad x \geq 6
\]
### Graphing the Solution:
To graph this solution on a number line:
1. Draw a number line.
2. Mark the points -1 and 6.
3. Use a closed circle at -1 (since -1 is included) and a closed circle at 6 (since 6 is included).
4. Shade to the left of -1 (representing all values less than or equal to -1) and shade to the right of 6 (representing all values greater than or equal to 6).
#### Textual Representation of the Number Line:
```
<===●========|=======●===>
-1 0 6
```
Where:
- The filled circle at -1 indicates that -1 is part of the solution.
- The filled circle at 6 indicates that 6 is part of the solution.
- The shading extends to the left of -1 and to the right of 6, indicating all values that satisfy the inequalities.
If you have more questions or need further clarification, feel free to ask!
### Given Inequalities:
1. \(-x - 3 \geq -2\)
2. \(-x - 3 \leq -9\)
### Solve the First Inequality:
\(-x - 3 \geq -2\)
1. **Add 3 to both sides**:
\[
-x \geq -2 + 3
\]
\[
-x \geq 1
\]
2. **Multiply by -1** (remember to reverse the inequality sign):
\[
x \leq -1
\]
### Solve the Second Inequality:
\(-x - 3 \leq -9\)
1. **Add 3 to both sides**:
\[
-x \leq -9 + 3
\]
\[
-x \leq -6
\]
2. **Multiply by -1** (again, reverse the inequality sign):
\[
x \geq 6
\]
### Combined Solution:
From the results, we have:
- First inequality: \( x \leq -1 \)
- Second inequality: \( x \geq 6 \)
The solution can be expressed as:
\[
x \leq -1 \quad \text{or} \quad x \geq 6
\]
### Graphing the Solution:
To graph this solution on a number line:
1. Draw a number line.
2. Mark the points -1 and 6.
3. Use a closed circle at -1 (since -1 is included) and a closed circle at 6 (since 6 is included).
4. Shade to the left of -1 (representing all values less than or equal to -1) and shade to the right of 6 (representing all values greater than or equal to 6).
#### Textual Representation of the Number Line:
```
<===●========|=======●===>
-1 0 6
```
Where:
- The filled circle at -1 indicates that -1 is part of the solution.
- The filled circle at 6 indicates that 6 is part of the solution.
- The shading extends to the left of -1 and to the right of 6, indicating all values that satisfy the inequalities.
If you have more questions or need further clarification, feel free to ask!
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