Which of the following equations have exactly one solution? Choose all answers that apply: A:58x+52=78x−78 B:−78x+52=−52x−78 C:52x+52=52x−78 D:58x+52=−78x−78

For this case we solve each of the equations:Option A:[tex]58x+52=78x-78\\58x-78x= -78-52\\-20x = -130[/tex][tex]x = \frac {-130} {- 20}\\x = \frac {13} {2}[/tex]It has a solution!Option B:[tex]-78x + 52 =-52x-78\\-78x + 52x=-78-52\\-26x = -130[/tex][tex]x=\frac{-130}{-26}\\\\x=5[/tex]It has a solution!Option C:[tex]52x + 52=52x-78\\52x-52 = -78-52\\0 = -130[/tex]The equation has no solution!Option D:[tex]58x + 52=-78x-78\\58x + 78x = -78-52\\136x = -130[/tex][tex]x = - \frac{130} {136}\\x = - \frac{65} {68}[/tex]It has a solution!Answer:Option A, B, D