Question

Which of the following is an example of an equation with exactly one solution?(1 point)
3x+4=4x+3
4x+3=4x+3
3x+4=3x+3
3x+4=3x+4

Answer 1

Are you sure? Because last time you made me miss three questions, incorrect.

Answer 2

To determine which of the given equations has exactly one solution, we can analyze each equation:

1. **\(3x + 4 = 4x + 3\)**
Rearranging gives:
\(3x + 4 - 4x = 3\)
\(-x + 4 = 3\)
\(-x = 3 - 4\)
\(-x = -1\)
\(x = 1\)
This equation has exactly one solution, \(x = 1\).

2. **\(4x + 3 = 4x + 3\)**
This is true for all values of \(x\) (an identity), so it has infinitely many solutions.

3. **\(3x + 4 = 3x + 3\)**
Rearranging gives:
\(3x + 4 - 3x = 3\)
\(4 = 3\)
This is a contradiction, so there are no solutions.

4. **\(3x + 4 = 3x + 4\)**
This is also true for all values of \(x\) (another identity), so it has infinitely many solutions.

Based on the above analysis, the equation with exactly one solution is:

**\(3x + 4 = 4x + 3\)**.

Answer 3

I apologize for any confusion, and I appreciate your patience. Let's carefully analyze each equation again step by step to ensure clarity:

1. **\(3x + 4 = 4x + 3\)**
Rearranging gives:
\(3x + 4 - 4x = 3\)
\(-x + 4 = 3\)
\(-x = 3 - 4\)
\(-x = -1\)
Therefore, \(x = 1\). This equation has **exactly one solution**.

2. **\(4x + 3 = 4x + 3\)**
This equation is always true for any value of \(x\), so it has **infinitely many solutions**.

3. **\(3x + 4 = 3x + 3\)**
Rearranging gives:
\(3x + 4 - 3x = 3\)
\(4 = 3\). This is a contradiction, meaning there are **no solutions**.

4. **\(3x + 4 = 3x + 4\)**
This equation is also always true for any value of \(x\), which means it has **infinitely many solutions** as well.

From this analysis, the equation with **exactly one solution** is indeed:

**\(3x + 4 = 4x + 3\)**.

If you have any additional equations or need further clarification, I'm here to help!