Question

Which of the following equations have exactly one solution?

Choose all answers that apply:
Choose all answers that apply:
(Choice A)
\[19x+18=-19x+18\]
A
\[19x+18=-19x+18\]
(Choice B)
\[-19x-18=-19x+18\]
B
\[-19x-18=-19x+18\]
(Choice C)
\[19x-18=-19x+18\]
C
\[19x-18=-19x+18\]
(Choice D)
\[-19x+18=-19x+18\]
D
\[-19x+18=-19x+18\]

Answer 1

A and C

Explanation:

A.

19x + 18 = -19x + 18

19x + 18 - 18 = -19x + 18 - 18

19x = -19x

19x + 19x = -19x + 19x

38x = 0

x = 0

this has only one solution

B.

-19x - 18 = -19x + 18

-19x - 18 + 18 = -19x + 18 + 18

-19x = -19x + 36

-19x + 19x = -19x + 19x + 36

0x = 36

0 =/= 36

no solution; the equations are parallel

C.

19x - 18 = -19x + 18

19x - 18 + 18 = -19x + 18 + 18

19x = -19x + 36

19x + 19x = -19x + 19x + 36

38x = 36

x = 36/38

exactly one solution

D.

-19x + 18 = -19x + 18

-19x + 18 - 18 = -19x + 18 - 18

-19x = -19x

-19x / -19 = -19x / -19

x = x

infinite number of solutions