Answer:
Options B and D
Step-by-step explanation:
Let's solve each equation:
x-3x=-2x+4
-2x=-2x+4
0=4
No solutions, so A is wrong
x-1/3(3x)=0
x-(3x/3)=0
x-x=0
0=0
Infinitely many solutions, so B is correct
1/3x-3=4+2x
1/3x=7+2x
-5/3x=7
x=-21/5
One solution, so C is incorrect
3x+2-1/3(3x)=2+2x
3x+2-(3x/3)=2+2x
3x+2-x=2+2x
2x+2=2+2x
2x=2x
0=0
Infinitely many solutions, so D is correct
x-1/3x+2=0
2/3x+2=0
2/3x=-2
x=3
One solution, so E is incorrect
As you can see, when both sides of the equations are equal to each other such as 0=0 and x=x, you'll always have infinitely many solutions. Therefore, options B and D are correct
