Is the Definition of Absolute Value Always True?

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In summary, the absolute value of a number is its distance from 0 on a number line, always resulting in a positive value. To find the absolute value of a number, the sign can be ignored and only the numerical value considered. The absolute value of 0 is 0, and it is slightly different from the concept of magnitude which refers to the size or amount of something. Absolute value is used in various real-life situations, including calculating distance, solving equations, and understanding the concept of positive and negative numbers.
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mathdad
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The definition of absolute value states the following:

| x | = x when x is > or = 0

| x | = -x when x < 0

I can use the above definition to rewrite expressions that do not contain absolute values.

| x - 3 |, where x < 3

If x < 3, then we can say that (x - 3) is less than 0.

So, -(x - 3) = -x + 3 = (3 - x).

Correct?
 
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Yes, for x< 3, |x- 3|= 3- x. For example, if x= 2, |2- 3|= |-1|= 1= 3- 2.

And, of course, if \(\displaystyle x\ge 3\), |x- 3|= x- 3.
 

Related to Is the Definition of Absolute Value Always True?

1. What is the definition of absolute value?

The absolute value of a number is its distance from 0 on a number line. It is always a positive value.

2. How do you find the absolute value of a number?

To find the absolute value of a number, you can ignore the sign and only consider the numerical value. For example, the absolute value of -5 is 5, and the absolute value of 7 is 7.

3. What is the absolute value of 0?

The absolute value of 0 is 0. This is because 0 is already at 0 distance from 0 on a number line, so it does not change when calculating absolute value.

4. What is the difference between absolute value and magnitude?

Absolute value and magnitude are similar concepts, but there is a slight difference. Magnitude refers to the size or amount of something, while absolute value specifically refers to the numerical distance from 0. For example, the magnitude of a vector is its length, while the absolute value of -3 is 3.

5. How is absolute value used in real life?

Absolute value is used in many real-life situations, such as calculating distance or speed, determining temperature changes, and solving mathematical equations. It is also important in understanding the concepts of positive and negative numbers and their relationships.

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