Chapter 1.4, Problem 54E

To determine

To complete: the give statement with always, sometimes or never.

Answer to Problem 54E

If a and b are real numbers, then $|a-b|$ is always equal to $|b-a|$

Explanation of Solution

Given:

If a and b are real numbers, then $|a-b|$ is--------------equal to $|b-a|$

Calculation:

In solving absolute value equations, remember that $|ax+b|=c\mid$ provided that $c\ge 0$ will either be:

  $ax+b=c\text{ or }ax+b=-c$

Note that when $c<0,$ the equation has no solution because absolute values are alwayspositive.

Since the absolute value of the difference of two numbers will always be positive, then changing the numbers' order and getting the absolute value of it will have the same value. Therefore, the answer is always.

If a and b are real numbers, then $|a-b|$ is always equal to $|b-a|$

Conclusion:

If a and b are real numbers, then $|a-b|$ is always equal to $|b-a|$