Question

Which of the following equations has exactly one solution?(1 point)
Responses

5x+4=5x+4
5
x
+
4
=
5
x
+
4
5 x plus 4 equals 5 x plus 4

−5x+4=5x+4
−
5
x
+
4
=
5
x
+
4
negative 5 x plus 4 equals 5 x plus 4

5x+4=5x+3
5
x
+
4
=
5
x
+
3
5 x plus 4 equals 5 x plus 3

−5x+3=−5x+3

Answer 1

To determine which equation has exactly one solution, let's analyze each option:

1. **5x + 4 = 5x + 4**: This equation simplifies to **0 = 0**, which is true for all values of x. Therefore, it has an infinite number of solutions.

2. **-5x + 4 = 5x + 4**: Rearranging this gives:
- -5x - 5x = 4 - 4
- -10x = 0
- x = 0
This equation has exactly one solution: **x = 0**.

3. **5x + 4 = 5x + 3**: Rearranging gives:
- 5x - 5x + 4 = 3
- 4 = 3
This is a false statement, and thus has no solutions.

4. **-5x + 3 = -5x + 3**: This simplifies to **0 = 0**, which is true for all values of x. Therefore, it has an infinite number of solutions.

Among the given equations, the one that has exactly one solution is:

**−5x + 4 = 5x + 4**.