Question

For which equations below is x = –3 a possible solution? Check all that apply.

|x| = 3

|x| = –3

|–x| = 3

|–x| = –3

–|x| = –3

–|x| = 3

Answer 1

Correct are the first, the third, and the fifth

Answer 2

The correct options are A, C and E.

Explanation

If a absolution equation is defined as

`|x|=a`

Then the solutions of the equation are x=a and x=-a.

A.

`|x|=3`

`x=\pm 3`

So,x=-3 is a solution of this equation.

B.

`|x|=-3`

This equation has no solution because the value of |x| can no

be negative.

C.

`|-x|=3`

`-x=\pm 3`

`x=\pm 3`

So,x=-3 is a solution of this equation.

D.

`|-x|=-3`

This equation has no solution because the value of |-x| can no

be negative.

E.

`-|x|=-3`

Divide both sides by -1.

`|x|=3`

`x=\pm 3`

So,x=-3 is a solution of this equation.

F.

`-|x|=3`

Divide both sides by -1.

`|x|=-3`

This equation has no solution because the value of |x| can not be negative.

Therefore the correct options are A, C and E.