True or False

Algebra Level 2

True or False?

For real numbers $a, b, c,$ and $d$ , if $a<b$ , and $c<d$ , then $(a-b) < (c-d)$ .

False, it will never be correct False, it is only sometimes correct True, it must be correct

1 solution

Marta Reece
Jun 21, 2017

The following two examples satisfy $a<b$ and $c<d$ and provide the opposite outcome when $a-b$ is compared to $c-d$

Example1: $a=0, b=1$ and $c=0, d=2$ will lead to $a-b=-1>-2=c-d$

Example2: $a=0, b=2$ and $c=0, d=1$ will lead to $a-b=-2<-1=c-d$

It is therefore not possible to determine the relationship between $a-b$ and $c-d$ from the two relationships given.