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

Question

Responses

−5x+4=5x+4
negative 5 x plus 4 is equal to 5 x plus 4 - no response given

5x+4=5x+4
5 x plus 4 is equal to 5 x plus 4 - incorrect

5x+4=5x+3
5 x plus 4 is equal to 5 x plus 3 - no response given

−5x+3=−5x+3

Answer 1

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

1. −5x + 4 = 5x + 4

   • Rearranging gives:
     • −5x - 5x = 4 - 4
     • −10x = 0
     • x = 0
   • This equation has exactly one solution: x = 0.

2. 5x + 4 = 5x + 4

   • Both sides are identical; thus, this equation holds for all x.
   • It has infinitely many solutions.

3. 5x + 4 = 5x + 3

   • Rearranging gives:
     • 5x - 5x = 3 - 4
     • 0 = -1
   • This is a contradiction; therefore, there are no solutions.

4. −5x + 3 = −5x + 3

   • Just like the second option, both sides are identical.
   • This equation holds for all x and has infinitely many solutions.

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

−5x + 4 = 5x + 4 (which leads to x = 0).