Chapter 5.3, Problem 67STP

To determine

To identify: The statement $ab>ac$ is always, sometimes or never true.

Answer to Problem 67STP

The statement $ab>ac$ is always true

Explanation of Solution

Given information: a, b and c are real numbers, $a\ne 0$ and $b>c$

Explanation: The statement $ab>ac$ is always true.

Given: $b>c$

Multiply both sides by a, then the resultant is $ab>ac$

Now, if $b>c$ , is always true then the above condition, $ab>ac$ is always true.

This can be explained by considering the examples:

1. Let $a=3,b=5,c=4$ according to the given condition.

Now, by calculating ab and ac,

  $ab=15$ and $ac=12$

which proves that $ab>ac$

2. Now, consider 1 more example, let $a=6,b=5,c=4$ according to the given condition.

By calculating, ab and ac,

  $ab=30$ and $ac=24$

which also proves that $ab>ac$

Thus, the condition $ab>ac$ is always true if $a\ne 0$ and $b>c$