Chapter 2.3, Problem 35E

(a)

To determine

To write: an inequality relating A and B.

Answer to Problem 35E

The inequality: $B<A$

Explanation of Solution

Given:

  

Calculation:

Write an inequality relating A and B:

  $B<A$

Conclusion:

The inequality: $B<A$

(b)

To determine

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

Answer to Problem 35E

The inequality: $-B>-A$

Explanation of Solution

Given:

  

Calculation:

Write an inequality relating - A and -B, using the position of numbers on the number line:

  $-B>-A$

Conclusion:

The inequality:

  $-B>-A$

(c)

To determine

To explain: the reason for reversing the direction of the

Answer to Problem 35E

If on the number line a number $a$ is smaller than a number $b$ , then the opposite of $a$ is bigger than the opposite of $b$

Explanation of Solution

Given:

  

Calculation:

If on the number line a number $a$ is smaller than a number $b$ , then the opposite of $a$ is bigger than the opposite of $b$ :

  $a<b\Rightarrow -a>-b$

This is equivalent to multiplying both sides of the inequality by -1.

Conclusion:

If on the number line a number $a$ is smaller than a number $b$ , then the opposite of $a$ is bigger than the opposite of $b$