Answer:
B, D
Step-by-step explanation:
Solve all equations:
A.
[tex]x-3x=-2x+4\\ \\-2x=-2x+4\\ \\0=4[/tex]
This is false equality, so this equation has no solutions.
B.
[tex]x-\dfrac{1}{3}(3x)=0\\ \\x-x=0\\ \\0=0[/tex]
This equality is true for all values of x, so this equation has infinitely many solutions.
C.
[tex]\dfrac{1}{3}x-3=4+2x\\ \\x-9=12+6x\\ \\x-6x=12+9\\ \\-5x=21\\ \\x=-\dfrac{21}{5}[/tex]
This equation has the unique solution.
D.
[tex]3x+2-\dfrac{1}{3}(3x)=2+2x\\ \\9x+6-3x=6+6x\\ \\6x+6=6+6x\\ \\0=0[/tex]
This equality is true for all values of x, so this equation has infinitely many solutions.
E.
[tex]x-\dfrac{1}{3}x+2=0\\ \\3x-x+6=0\\ \\2x=-6\\ \\x=-3[/tex]
This equation has the unique solution.
