Chapter 1.4, Problem 53E

To determine

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

Answer to Problem 53E

If $x^2=a^2,$ then $\left|x\right|$ is always equal to $\left|a\right|$

Explanation of Solution

Given:

If $x^2=a^2,$ then $\left|x\right|$ is -----------equal to $\left|a\right|$

Calculation:

If $x^2$ equals $a^2,$ then $x=a.$ Therefore, $x$ and a will have the same absolute values, too, no matter what value they are.

If $x^2=a^2,$ then $\left|x\right|$ is always equal to $\left|a\right|$

Conclusion:

If $x^2=a^2,$ then $\left|x\right|$ is always equal to $\left|a\right|$