Chapter 2.3, Problem 35E

a.

To determine

To write: an inequality relating A and B .

Answer to Problem 35E

  $A>B$ Or $B<A$

Explanation of Solution

Consider the given number line:

  

Clearly, A is greater than B .

So, an inequality relating A and B is $A>B$ or $B<A$ .

b.

To determine

To write: an inequality relating $-A$ and $-B$ .

Answer to Problem 35E

  $-B>-A$ or $-A<-B$

Explanation of Solution

Consider the given number line:

  

Clearly, $-B$ is greater than $-A$ .

So, an inequality relating $-A$ and $-B$ is $-B>-A$ or $-A<-B$ .

c.

To determine

To explain: why inequality sign must be reversed when dividing or multiplying each side of inequality by same negative number.

Answer to Problem 35E

As numbers moves away from 0, their absolute value increases.

Explanation of Solution

From part (a), $A>B$ or $B<A$

From part (b), $-A<-B$ or $-B>-A$ .

It can be observed that on multiplying by -1 on each side, the signs of inequality are reversed.

It can be said that as numbers moves away from 0, their absolute value increases.

  $A>B\Rightarrow \left|A\right|>\left|B\right|$

  $-A<-B\Rightarrow \left|A\right|>\left|B\right|$