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.

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