Which of the following equations has no solutions?(1 point)

Question

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 6 x plus 3

6x+4=6x+4
6 x plus 4 equals 6 x plus 4

−6x+4=−6x+3

GPT-4o mini · Answer

To determine which of the equations has no solutions, we can simplify each one:

$6 x + 3 = - 6 x + 3$
Combine like terms:
$6 x + 6 x = 3 - 3$
$12 x = 0$
$x = 0$
(This has a solution: $x = 0$ )
$- 6 x + 4 = 6 x + 3$
Combine like terms:
$- 6 x - 6 x = 3 - 4$
$- 12 x = - 1$
$x = \frac{1}{12}$
(This has a solution: $x = \frac{1}{12}$ )
$6 x + 4 = 6 x + 4$
This simplifies to $0 = 0$ , which is true for all values of $x$ .
(This has infinitely many solutions.)
$- 6 x + 4 = - 6 x + 3$
Combine like terms:
$- 6 x + 6 x = 3 - 4$
$0 = - 1$
(This is a contradiction and has no solutions.)

The equation that has no solutions is $- 6 x + 4 = - 6 x + 3$ .