Hello, the answer should be A,B and D options.
First, let's edit the given equations option-by-option.
Option A:
[tex]-5x+12=5x+12[/tex]
[tex]-5x-5x=-12+12[/tex]
[tex]-10x=0[/tex]
[tex]x=0[/tex]
There is only one solution which is [tex]x=0[/tex].
Option B:
[tex]-5x+12=5x-5[/tex]
[tex]-5x-5x=-12-5[/tex]
[tex]-10x=-17[/tex]
[tex]x=\frac{17}{10}[/tex]
There is only one solution which is [tex]x=\frac{17}{10}[/tex].
Option C:
[tex]-5x+12=-5x-12[/tex]
[tex]-5x+5x=-12-12[/tex]
[tex]0\neq -24[/tex]
In Math, zero is not equal to minus twenty four ([tex]0\neq -24[/tex]) that's why we do not have any solution in this equation.
Option D:
[tex]-5x+12=-12x-12[/tex]
[tex]-5x+12x=-12-12[/tex]
[tex]7x=-24[/tex]
[tex]x=-(\frac{24}{7} )[/tex]
There is only one solution which is [tex]x=-(\frac{24}{7} )[/tex]
