Question

Which of the following equations have exactly one solution?

Choose all answers that apply:
Choose all answers that apply:

(Choice A)
A
19x+18=-19x+18


B 19x-18=-19x+18
(Choice C)
C
-19x-18=-19x+18

(Choice D)
D
-19x+18=-19x+18
Please Answer ASAP

Answer 1

A and C

Explanation:

Answer 2

For choice A, we can rearrange the equation to
`38x=0,` so it has exactly one solution,
`x=0.`

For choice B, we rearrange the equation to
`38x=36,` so this too has exactly one solution,
`x=(36)/(38)=(18)/(19).`

Rearranging the equation in choice C by eliminating the
`x` terms gives us the false equality
`-18=18,` so this equation has no solutions.

Eliminating
`x` in the equation in choice D gives the equality
`18=18,` which is always true, so this equation has infinitely many solutions.

Thus, we conclude that choices A and B work.