Question

Help thank you Decide if this statement is true or false x = 2 if and only is |x|=2

Answer 1

False

Explanation:

The statement "if and only if" is a conditional statement which goes both ways, meaning that if a is true then b is true, and if b is true then a is true. So if x=2 is true than | x | =2 is true, but if | x | =2 is true, that does not necessarily mean that x=2 is true. For example, if x is -2 than the statement | x | =2 is true, but x=2 is false.

If x=2 is true then | x |=2 is true

If | x |=2 is true then x=2 may be true or false

You can prove this with math.

If x=2, find | x |=2

| 2 |=2

2=2 True

If | x |=2, find x=2

| x |=2

x=2,-2

Put in 2 and -2 in for x

2=2 True

-2=2 False

Therefore it cannot be determined

Sorry if this is confusing, hope it helps.

Answer 2

I believe the answer is true.

Explanation:

So if the absolute value of x is two then x could be two things. It could either be two or negative two.