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

Question

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.