Pleeaase help. Select ALL the correct answers

Which equations have infinitely many solutions?

The 1st, 3rd and 4th

Step-by-step explanation:

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