Question

If x < y, then all of the following are true except _____.

x/2 < x/2
- x < - y
x + 2 < y + 2
2 x < 2 y

Answer 1

the first one because they are both x.

Explanation:

Answer 2

`(x)/(2) < (x)/(2)`

`-x < -y`

These expressions are not true.

Explanation:

The first option is not true, because is
`x<y`, it implies that
`(x)/(2) <(y)/(2)`. Also, there doesn't exist a number that is reflexive regarding < or > relations, because a number is not more or less than itself, the reflexive property is applied with equalities, or
`\leq \geq` relations, because the equality signs is included.

The other expression that is not true is the second one, because when we multiply or divide a negative number in a inequality, the relations changes, for example:

`-x<-y\\(-x)/(-1)<(-y)/(-1)\\x>y`

As you can see, the relations changed from < to >, demonstrating that is not true.

Therefore the first and second options are false.