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

Answers

Answered by Emma Grace Hoagland
wrong
Answered by 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
Answered by 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:

**\(-3x - 8 = 3x - 8\)**.
Answered by 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!
Answered by 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:**

**\(−3x − 8 = 3x − 8\)**.

Related Questions