Answer:
Equation 1 has no solution.
Step-by-step explanation:
We are given the following information in the question:
We evaluate the given expressions to find which equations have no solution.
1)
[tex]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}[/tex]
2)
[tex]3(x-2)+x=4x-6\\3x -6 + x= 4x - 6\\4x - 6 = 4x - 6\\\text{The above equation has infinitely many solutions}[/tex]
3)
[tex]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}[/tex]
4)
[tex]3(x-2)+x=3x-3\\3x -6 + x= 3x - 3\\4x - 6 = 3x - 3\\x = 3\\\text{The above equation has unique solution}[/tex]
Equation 1 has no solution.
