Question

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 4x+3=4x+3 4 x plus 3 equals 4 x plus 3 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

Answer 1

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

1. **\(3x + 4 = 4x + 3\)**
Rearranging gives:
\(3x + 4 - 4x - 3 = 0\)
\(-x + 1 = 0\)
This has one solution: \(x = 1\).

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

3. **\(3x + 4 = 3x + 4\)**
Like the previous one, this equation is always true for any \(x\) and has infinitely many solutions.

4. **\(3x + 4 = 3x + 3\)**
Rearranging gives:
\(3x + 4 - 3x - 3 = 0\)
\(1 = 0\)
This is a contradiction, so it has no solutions.

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

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