Question

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

Answer 1

For this case we solve each of the equations:

Option A:

$58x+52=78x-78\\58x-78x= -78-52\\-20x = -130$

$x = \frac {-130} {- 20}\\x = \frac {13} {2}$

It has a solution!

Option B:

$-78x + 52 =-52x-78\\-78x + 52x=-78-52\\-26x = -130$

$x=\frac{-130}{-26}\\\\x=5$

It has a solution!

Option C:

$52x + 52=52x-78\\52x-52 = -78-52\\0 = -130$

The equation has no solution!

Option D:

$58x + 52=-78x-78\\58x + 78x = -78-52\\136x = -130$

$x = - \frac{130} {136}\\x = - \frac{65} {68}$

It has a solution!

Answer:

Option A, B, D

Answer 2

Answer:

A,B,C

Step-by-step explanation: