Asked by indyy
yo
Which of the following is an example of an equation with no solution?(1 point)
Responses
3x+4=3x+4
3 x plus 4 equals 3 x plus 4
3x+4=3x+3
3 x plus 4 equals 3 x plus 3
3x+4=4x+3
3 x plus 4 equals 4 x plus 3
4x+3=3x+3
Which of the following is an example of an equation with no solution?(1 point)
Responses
3x+4=3x+4
3 x plus 4 equals 3 x plus 4
3x+4=3x+3
3 x plus 4 equals 3 x plus 3
3x+4=4x+3
3 x plus 4 equals 4 x plus 3
4x+3=3x+3
Answers
Answered by
indyy
Which of the following is an example of an equation with exactly one solution?(1 point)
Responses
3x+4=4x+3
3 x plus 4 equals 4 x plus 3
3x+4=3x+3
3 x plus 4 equals 3 x plus 3
3x+4=3x+4
3 x plus 4 equals 3 x plus 4
4x+3=4x+3
Responses
3x+4=4x+3
3 x plus 4 equals 4 x plus 3
3x+4=3x+3
3 x plus 4 equals 3 x plus 3
3x+4=3x+4
3 x plus 4 equals 3 x plus 4
4x+3=4x+3
Answered by
indyy
Solve for x to determine if the equation has one, none, or infinite solutions.
3(x+2)−6=3x (1 point)
Responses
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=−3.
The equation has one solution: x equals negative 3 .
The equation has no solution.
The equation has no solution.
The equation has one solution: x=3.
3(x+2)−6=3x (1 point)
Responses
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=−3.
The equation has one solution: x equals negative 3 .
The equation has no solution.
The equation has no solution.
The equation has one solution: x=3.
Answered by
indyy
Solve for x to determine if the equation has one, none, or infinite solutions.
4x=3(x+5)−15 (1 point)
Responses
The equation has no solution.
The equation has no solution.
The equation has one solution: x=0.
The equation has one solution: x equals 0 .
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=−10.
4x=3(x+5)−15 (1 point)
Responses
The equation has no solution.
The equation has no solution.
The equation has one solution: x=0.
The equation has one solution: x equals 0 .
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=−10.
Answered by
indyy
Solve for x to determine if the equation has one, none, or infinite solutions.
5(2x+2)−7x=3x+6 (1 point)
Responses
The equation has no solution.
The equation has no solution.
The equation has one solution: x=6.
The equation has one solution: x equals 6 .
The equation has one solution: x=10.
The equation has one solution: x equals 10 .
The equation has infinite solutions.
5(2x+2)−7x=3x+6 (1 point)
Responses
The equation has no solution.
The equation has no solution.
The equation has one solution: x=6.
The equation has one solution: x equals 6 .
The equation has one solution: x=10.
The equation has one solution: x equals 10 .
The equation has infinite solutions.
Answered by
GPT-4o mini
To determine which equation has no solution, we can analyze each option:
1. **\(3x + 4 = 3x + 4\)**: This is true for all \(x\) (an identity), so it has infinitely many solutions.
2. **\(3x + 4 = 3x + 3\)**: If we subtract \(3x\) from both sides, we get \(4 = 3\), which is false. Therefore, this equation has no solution.
3. **\(3x + 4 = 4x + 3\)**: If we rearrange the equation, we can move \(3x\) to the right side to get \(4 = x + 3\), leading to \(x = 1\). So this equation has one solution.
4. **\(4x + 3 = 3x + 3\)**: If we subtract \(3x\) from both sides, it reduces to \(x + 3 = 3\), leading to \(x = 0\). Therefore, this equation has one solution.
Based on this analysis, the equation with **no solution** is:
**\(3x + 4 = 3x + 3\)**.
1. **\(3x + 4 = 3x + 4\)**: This is true for all \(x\) (an identity), so it has infinitely many solutions.
2. **\(3x + 4 = 3x + 3\)**: If we subtract \(3x\) from both sides, we get \(4 = 3\), which is false. Therefore, this equation has no solution.
3. **\(3x + 4 = 4x + 3\)**: If we rearrange the equation, we can move \(3x\) to the right side to get \(4 = x + 3\), leading to \(x = 1\). So this equation has one solution.
4. **\(4x + 3 = 3x + 3\)**: If we subtract \(3x\) from both sides, it reduces to \(x + 3 = 3\), leading to \(x = 0\). Therefore, this equation has one solution.
Based on this analysis, the equation with **no solution** is:
**\(3x + 4 = 3x + 3\)**.
Answered by
GPT-4o mini
To find the equation with exactly one solution, let's analyze each option:
1. **\(3x + 4 = 4x + 3\)**: Rearranging gives \(4 - 3 = x\) or \(x = 1\). This equation has **exactly one solution**.
2. **\(3x + 4 = 3x + 3\)**: This simplifies to \(4 = 3\), which is false. Thus, it has **no solution**.
3. **\(3x + 4 = 3x + 4\)**: This is true for all \(x\), meaning it has **infinitely many solutions**.
4. **\(4x + 3 = 4x + 3\)**: Similar to the previous one, this is true for all \(x\), leading to **infinitely many solutions**.
Based on this analysis, the equation that has **exactly one solution** is:
**\(3x + 4 = 4x + 3\)**.
1. **\(3x + 4 = 4x + 3\)**: Rearranging gives \(4 - 3 = x\) or \(x = 1\). This equation has **exactly one solution**.
2. **\(3x + 4 = 3x + 3\)**: This simplifies to \(4 = 3\), which is false. Thus, it has **no solution**.
3. **\(3x + 4 = 3x + 4\)**: This is true for all \(x\), meaning it has **infinitely many solutions**.
4. **\(4x + 3 = 4x + 3\)**: Similar to the previous one, this is true for all \(x\), leading to **infinitely many solutions**.
Based on this analysis, the equation that has **exactly one solution** is:
**\(3x + 4 = 4x + 3\)**.
Answered by
GPT-4o mini
Let's solve the equation \(3(x+2) - 6 = 3x\).
1. Distribute on the left side:
\[
3x + 6 - 6 = 3x
\]
Simplifying gives:
\[
3x = 3x
\]
2. This is an identity, meaning it is true for all values of \(x\). Therefore, the equation has **infinite solutions**.
Based on this, the correct response is:
**The equation has infinite solutions.**
1. Distribute on the left side:
\[
3x + 6 - 6 = 3x
\]
Simplifying gives:
\[
3x = 3x
\]
2. This is an identity, meaning it is true for all values of \(x\). Therefore, the equation has **infinite solutions**.
Based on this, the correct response is:
**The equation has infinite solutions.**
Answered by
GPT-4o mini
Let's solve the equation \(4x = 3(x + 5) - 15\).
1. Start by distributing on the right side:
\[
4x = 3x + 15 - 15
\]
2. Simplify the right side:
\[
4x = 3x + 0
\]
which simplifies to:
\[
4x = 3x
\]
3. Now, subtract \(3x\) from both sides:
\[
4x - 3x = 0
\]
This simplifies to:
\[
x = 0
\]
Since we found a specific value \(x = 0\), the equation has **one solution**.
Therefore, the correct response is:
**The equation has one solution: \(x=0\).**
1. Start by distributing on the right side:
\[
4x = 3x + 15 - 15
\]
2. Simplify the right side:
\[
4x = 3x + 0
\]
which simplifies to:
\[
4x = 3x
\]
3. Now, subtract \(3x\) from both sides:
\[
4x - 3x = 0
\]
This simplifies to:
\[
x = 0
\]
Since we found a specific value \(x = 0\), the equation has **one solution**.
Therefore, the correct response is:
**The equation has one solution: \(x=0\).**
Answered by
GPT-4o mini
Let's solve the equation \(5(2x + 2) - 7x = 3x + 6\).
1. Distribute on the left side:
\[
5 \cdot 2x + 5 \cdot 2 - 7x = 3x + 6
\]
This simplifies to:
\[
10x + 10 - 7x = 3x + 6
\]
2. Combine like terms on the left side:
\[
(10x - 7x) + 10 = 3x + 6
\]
This simplifies to:
\[
3x + 10 = 3x + 6
\]
3. Now, subtract \(3x\) from both sides:
\[
10 = 6
\]
Since \(10\) does not equal \(6\), this is a false statement, indicating that there is **no solution**.
Therefore, the correct response is:
**The equation has no solution.**
1. Distribute on the left side:
\[
5 \cdot 2x + 5 \cdot 2 - 7x = 3x + 6
\]
This simplifies to:
\[
10x + 10 - 7x = 3x + 6
\]
2. Combine like terms on the left side:
\[
(10x - 7x) + 10 = 3x + 6
\]
This simplifies to:
\[
3x + 10 = 3x + 6
\]
3. Now, subtract \(3x\) from both sides:
\[
10 = 6
\]
Since \(10\) does not equal \(6\), this is a false statement, indicating that there is **no solution**.
Therefore, the correct response is:
**The equation has no solution.**
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