Question

Felix wrote several equations and determined that only one of the equations has no solution. Which of these equations has no solution?

3(x-2)+x=4x+6

3(x-2)+x=4x-6

3(x-2)+x=2x-6

3(x-2)+x=3x-3

Answer 1

A. 3(x-2)+x=4x+6 has no solution.

Answer 2

Equation 1 has no solution.

Explanation:

We are given the following information in the question:

We evaluate the given expressions to find which equations have no solution.

1)

`3(x-2)+x=4x+6\\3x -6 + x= 4x + 6\\4x - 6 = 4x + 6\\-6 = 6\\\text{which is not possible}\\\text{The above equation has no solution}`

2)

`3(x-2)+x=4x-6\\3x -6 + x= 4x - 6\\4x - 6 = 4x - 6\\\text{The above equation has infinitely many solutions}`

3)

`3(x-2)+x=2x-6\\3x -6 + x= 2x - 6\\4x - 6 = 2x - 6\\2x = 0\\x = 0\\\text{The above equation has unique solution}`

4)

`3(x-2)+x=3x-3\\3x -6 + x= 3x - 3\\4x - 6 = 3x - 3\\x = 3\\\text{The above equation has unique solution}`

Equation 1 has no solution.