Question
wrong
Which of the following equations has exactly one solution?(1 point) Responses −8x+3=−8x+3 negative 8 x plus 3 equals negative 8 x plus 3 −3x+8=−3x−8 negative 3 x plus 8 equals negative 3 x minus 8 3x−8=3x+8 3 x minus 8 equals 3 x plus 8 −3x−8=3x−8
Which of the following equations has exactly one solution?(1 point) Responses −8x+3=−8x+3 negative 8 x plus 3 equals negative 8 x plus 3 −3x+8=−3x−8 negative 3 x plus 8 equals negative 3 x minus 8 3x−8=3x+8 3 x minus 8 equals 3 x plus 8 −3x−8=3x−8
Answers
GPT-4o mini
To determine which of the given equations has exactly one solution, we can analyze each option:
1. **\(-8x + 3 = -8x + 3\)**:
- This is an identity; both sides are equal for all values of \(x\). (Infinite solutions)
2. **\(-3x + 8 = -3x - 8\)**:
- If we simplify this equation:
\(-3x + 8 + 3x = -8\) ⟹ \(8 = -8\) (Contradiction)
- This means there are no solutions.
3. **\(3x - 8 = 3x + 8\)**:
- If we simplify this equation:
\(3x - 3x - 8 = 8\) ⟹ \(-8 = 8\) (Contradiction)
- This means there are no solutions.
4. **\(-3x - 8 = 3x - 8\)**:
- If we simplify this equation:
\(-3x - 8 - 3x = -8\) ⟹ \(-6x = 0\) ⟹ \(x = 0\) (One solution)
From the choices above, the equation that has exactly one solution is:
**\(-3x - 8 = 3x - 8\)**.
1. **\(-8x + 3 = -8x + 3\)**:
- This is an identity; both sides are equal for all values of \(x\). (Infinite solutions)
2. **\(-3x + 8 = -3x - 8\)**:
- If we simplify this equation:
\(-3x + 8 + 3x = -8\) ⟹ \(8 = -8\) (Contradiction)
- This means there are no solutions.
3. **\(3x - 8 = 3x + 8\)**:
- If we simplify this equation:
\(3x - 3x - 8 = 8\) ⟹ \(-8 = 8\) (Contradiction)
- This means there are no solutions.
4. **\(-3x - 8 = 3x - 8\)**:
- If we simplify this equation:
\(-3x - 8 - 3x = -8\) ⟹ \(-6x = 0\) ⟹ \(x = 0\) (One solution)
From the choices above, the equation that has exactly one solution is:
**\(-3x - 8 = 3x - 8\)**.
Emma Grace Hoagland
wrong
GPT-4o mini
I apologize for the confusion in my previous response. Let's reevaluate the equations to find out which one has exactly one solution.
1. **\(-8x + 3 = -8x + 3\)**:
- This simplifies to \(0 = 0\), which is true for all \(x\) (infinite solutions).
2. **\(-3x + 8 = -3x - 8\)**:
- If we simplify this, we have:
\(-3x + 8 + 3x = -8\) ⟹ \(8 = -8\) (this is a contradiction, therefore no solutions).
3. **\(3x - 8 = 3x + 8\)**:
- Simplifying this gives:
\(3x - 3x - 8 = 8\) ⟹ \(-8 = 8\) (this is also a contradiction, therefore no solutions).
4. **\(-3x - 8 = 3x - 8\)**:
- Simplifying this gives:
\(-3x - 8 - 3x = -8\) ⟹ \(-6x - 8 = -8\) ⟹ \(-6x = 0\) ⟹ \(x = 0\) (one solution).
Based on this analysis, only the fourth equation **\(-3x - 8 = 3x - 8\)** has exactly one solution, which is \(x = 0\).
If this still doesn't align with what you're looking for, please let me know the correct answer or provide further clarification!
1. **\(-8x + 3 = -8x + 3\)**:
- This simplifies to \(0 = 0\), which is true for all \(x\) (infinite solutions).
2. **\(-3x + 8 = -3x - 8\)**:
- If we simplify this, we have:
\(-3x + 8 + 3x = -8\) ⟹ \(8 = -8\) (this is a contradiction, therefore no solutions).
3. **\(3x - 8 = 3x + 8\)**:
- Simplifying this gives:
\(3x - 3x - 8 = 8\) ⟹ \(-8 = 8\) (this is also a contradiction, therefore no solutions).
4. **\(-3x - 8 = 3x - 8\)**:
- Simplifying this gives:
\(-3x - 8 - 3x = -8\) ⟹ \(-6x - 8 = -8\) ⟹ \(-6x = 0\) ⟹ \(x = 0\) (one solution).
Based on this analysis, only the fourth equation **\(-3x - 8 = 3x - 8\)** has exactly one solution, which is \(x = 0\).
If this still doesn't align with what you're looking for, please let me know the correct answer or provide further clarification!
Emma Grace Hoagland
Which of the following equations has exactly one solution?(1 point) Responses −8x+3=−8x+3 negative 8 x plus 3 equals negative 8 x plus 3 −3x+8=−3x−8 negative 3 x plus 8 equals negative 3 x minus 8 3x−8=3x+8 3 x minus 8 equals 3 x plus 8 −3x−8=3x−8
GPT-4o mini
Let's analyze each equation step by step to determine which one has exactly one solution:
1. **\(−8x + 3 = −8x + 3\)**:
- This simplifies to \(0 = 0\), which is true for all \(x\). This has **infinite solutions.**
2. **\(−3x + 8 = −3x − 8\)**:
- If we simplify this, we get:
\[
-3x + 8 + 3x = -8 \implies 8 = -8
\]
- This is a contradiction and means there are **no solutions.**
3. **\(3x - 8 = 3x + 8\)**:
- Simplifying this gives:
\[
3x - 3x - 8 = 8 \implies -8 = 8
\]
- This is also a contradiction, resulting in **no solutions.**
4. **\(−3x − 8 = 3x − 8\)**:
- Simplifying this gives:
\[
-3x - 8 - 3x = -8 \implies -6x - 8 = -8 \implies -6x = 0 \implies x = 0
\]
- This equation has **exactly one solution**, which is \(x = 0\).
**Conclusion: The equation that has exactly one solution is:**
**\(−3x − 8 = 3x − 8\)**.
1. **\(−8x + 3 = −8x + 3\)**:
- This simplifies to \(0 = 0\), which is true for all \(x\). This has **infinite solutions.**
2. **\(−3x + 8 = −3x − 8\)**:
- If we simplify this, we get:
\[
-3x + 8 + 3x = -8 \implies 8 = -8
\]
- This is a contradiction and means there are **no solutions.**
3. **\(3x - 8 = 3x + 8\)**:
- Simplifying this gives:
\[
3x - 3x - 8 = 8 \implies -8 = 8
\]
- This is also a contradiction, resulting in **no solutions.**
4. **\(−3x − 8 = 3x − 8\)**:
- Simplifying this gives:
\[
-3x - 8 - 3x = -8 \implies -6x - 8 = -8 \implies -6x = 0 \implies x = 0
\]
- This equation has **exactly one solution**, which is \(x = 0\).
**Conclusion: The equation that has exactly one solution is:**
**\(−3x − 8 = 3x − 8\)**.