Integers involving absolute zero

[hmwin]

Can someone please help with the following question.

Assuming a is a non zero integer, which of the following statements is NEVER true:
1. a > -a
2. a < -a
3. [a] = -a
4. [a] = -[a]

We find that three of the answers could be correct (never true)... help!

 

[mmm4444bot]

Try an experiment ...

Please try the following.

First, let a = -10

Write out each equation and replace the symbol a with the value -10

(Be careful to pay attention to all of the negative signs.)

When the value of a is -10, which of the statements are true?

Now do the same thing with a = 10.

What do you discover?

Please post your results if you need more help with your exercise.

~ Mark

 

[hmwin]

Mark,
Assuming that this is the case: a > -a whereas a is -10... the formula would look like this -10 > - (-10) ,so -10 >10 which is false. Filling all of them in that way, I would find that the fourth option is never true. If that is the case, thanks so much for the help! I truly appreciate it!

 

[mmm4444bot]

Your experiment succeeded ...

... Filling all of them in that way, I would find that the fourth option is never true ...

You are correct.

|x| = |x| is always true.

|x| = -|x| is never true when x is non-zero.

There are two "skills" to this exercise.

The first has to do with a negative sign in front of a variable, like -a.

1) Never assume that -a is a negative quantity; I know it looks like it's negative, but the actual value depends entirely on whatever value we assign to a.

The second has to do with understanding absolute value.

2) Remember when you see |a| that it always refers to the magnitude of the value a. Magnitude is a distance (the distance away from zero on the number line), and distance is ALWAYS positive, regardless of whether you move away from zero to the left or to the right.

Cheers,

~ Mark

 

[Denis]

Hey buddy, why don't you go bump elsewhere :shock: