Question 972631

1. The absolute value of "{{{a}}}" is (never, sometimes, always) equal to "{{{a}}}".

The absolute value of {{{a}}}, denoted "{{{abs(a)}}} " is the distance of {{{a}}} from zero. This is why absolute value is {{{never}}}{{{ negative}}}; absolute value only asks "{{{how}}}{{{ far}}}?", not "{{{in}}}{{{ which}}}{{{ direction}}}?"

so, your answer is:
The absolute value of "{{{a}}}" is  {{{always}}} equal to "{{{a}}}"


2. The absolute value of "{{{x}}}" is (never, sometimes, always) equal to "{{{-x}}}".

since, by definition, absolute value is {{{never}}}{{{ negative}}}, your answer is:

The absolute value of "{{{x}}}" is {{{never}}} equal to "{{{-x}}}".



3. The absolute value of "{{{y}}}" is (never, sometimes, always) equal to a positive integer.

The absolute value of an integer is the numerical value without regard to whether the sign is negative or positive. {{{y}}} could be an integer, or decimal... 
The absolute value of "{{{y}}}" is {{{sometimes}}} equal to a positive integer.

4. "{{{x}}}" is {{{never}}} greater than "{{{x}}}".


5. Can you show the steps in the solutions to these problems?

steps shown above