Question

Which of the following equations have exactly one solution?

Answer 1

B

Explanation:

You can try to solve each:

A.
`2x - 31 = 2x - 31\\`

add 31 to both sides

`2x = 2x`

subtract 2x from both sides

`0 = 0`

This means infinite solutions

B.
`2x-31 = -2x-31`

add 31 to both sides

`2x = -2x`

add 2x to both sides

`4x = 0`

divide both sides by 4

`x = 0`

This does have one solution

C.
`2x + 31 = 2x-31`

subtract 31 from both sides

`2x = 2x-62`

subtract 2x from both sides

`0 = -62`

This is not true, so no solutions

D.
`2x -2 = 2x -31`

add 2 to both sides

`2x = 2x - 29`

subtract 2x from both sides

0 = -29

not true, so b is the answer.