Which of the following equations has no solutions?(1 point) Responses 6x+3=−6x+3 6 x plus 3 equals negative 6 x plus 3 −6x+4=−6x+3 negative 6 x plus 4 equals negative 6 x plus 3 6x+4=6x+4 6 x plus 4 equals 6 x plus 4 −6x+4=6x+3

Answer 1

To determine which of the equations has no solutions, we can analyze each equation:

1. \( 6x + 3 = -6x + 3 \)
   Rearranging gives:
   \( 6x + 6x = 3 - 3 \)
   \( 12x = 0 \)
   \( x = 0 \) (This has a solution.)

2. \( -6x + 4 = -6x + 3 \)
   Rearranging gives:
   \( 4 = 3 \) (This is a contradiction.)
   (This has no solutions.)

3. \( 6x + 4 = 6x + 4 \)
   This is an identity that is always true for all \( x \).
   (This has infinitely many solutions.)

4. \( -6x + 4 = 6x + 3 \)
   Rearranging gives:
   \( -6x - 6x = 3 - 4 \)
   \( -12x = -1 \)
   \( x = \frac{1}{12} \) (This has a solution.)

From the above analysis, the equation that has no solutions is:

\( -6x + 4 = -6x + 3 \)