Explain how Absolute Values work

Question

To understand the absolute value definition you must believe that IxI = -x for negative x's. using x=-3 as an example, explain in words why multiplying x by -1 produces the same result as taking the absolute value of x.

Answer 1

In plain English, absolute value is just a certain distance from 0. Since distance is always a positive value (e.g., you would not say you went -6 feet if you moonwalked to get to a door 6 feet away), absolute value must also be a positive value.

In your example, -3 is 3 units away from 0, so |-3| is 3. Likewise, multiplying a negative number by a negative number yields a positive product, and -3 * -1 = 3... which happens to be the same distance from 0 that we had gotten before. Thus, |-3| = (-3)(-1).

What Jim said was correct. For the person who might not appreciate the absolute value graph, however, perhaps the moonwalking illustration will suffice to get the concept to stick. (I will spare you a video answer.)

Good luck with your studies.

Answer 2

Hi Sam,

Belief has nothing to do with the absolute value function. The definition of ΙxΙ is x for x>=0 and -x for x<0

The graph of ΙxΙ is a "V" shape. Multiplying by -1 makes the value of the function >0 for x <0.

Hope this helps. If I have misunderstood your question let me know.

Regards

Jim