Respuesta :
Given:
The different equations in the options.
To find:
The equation which have infinitely many solutions.
Solution:
In option A,
[tex]2x+8=2(x+8)[/tex]
[tex]2x+8=2x+16[/tex]
[tex]8=16[/tex]
This statement is false for any real value of x. So, the given equation has no solution.
In option B,
[tex]3x+2(x-2)+6=5x+2[/tex]
[tex]3x+2x-4+6=5x+2[/tex]
[tex]5x+2=5x+2[/tex]
[tex]2=2[/tex]
This statement is true for all real value of x. So, the given equation has infinitely many solutions.
In option C,
[tex]x+7=7[/tex]
[tex]x=7-7[/tex]
[tex]x=0[/tex]
This equation has only one solution, i.e., x=0.
In option D,
[tex]x=0[/tex]
This equation has only one solution, i.e., x=0.
Only equation [tex]3x+2(x-2)+6=5x+2[/tex] has infinitely many solutions. Therefore, the correct option is B.
