Algebra Absolute Value?
The absolute value of x is the magnitude of x without its sign. (the absolute values of -1 and 1 are 1). Show how this absolute value can be used with addition and subtraction to find the larger value of twos.
Hint: The sign of a-b depends on which of a and b is larger.
My answer; if a is bigger than b, then the difference of a and b will be always positive. On the other hand, if b is bigger than a, the difference will be negative.
My question: Apparently, I need to add the absolute value of this difference to some values because it will get me closer to the desired result. Why do I have to do this? Can you just do what I did above? What is this "some values"? How can you figure out the larger value of two numbers by simply subtracting and adding?
Please explain. Thank you.
Comments
We need to use the absolute value function to tell us whether a or b is bigger than the other value.
Here's the answer. Using the hint, we see that if | a - b | = a - b, then a is greater than or equal to b. Otherwise, b is bigger.
For example, if a = 2 and b = 1, then | a - b| = | 2 - 1 | = | 1 | = 1 = 2 - 1 = a - b, so a is greater than or equal to b.
Another example, if a = 1 and b = 2, then | a - b | = | 1 - 2 | = | -1 | = 1 but a - b = -1, so b is bigger because | a - b | ≠ a - b in this case.