How Can Absolute Value Definitions Be Used to Rewrite Expressions?

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In summary, The absolute value of a number is its distance from zero on a number line and is always positive. To calculate it, remove the negative sign (if any). Absolute value and magnitude are similar but have different meanings. Absolute value can be a decimal or fraction and has many real-life applications, such as in physics, engineering, and finance.
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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^4 + 1 |

Since x^4 + 1 > 0, then the answer is simply the expression itself or x^4 + 1.

Correct?
 
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Yes, for all real numbers, x, [tex]|x^4+ 1|= x^4+ 1[/tex].
 

FAQ: How Can Absolute Value Definitions Be Used to Rewrite Expressions?

What is the definition of absolute value?

The absolute value of a number is its distance from zero on a number line. It is always a positive number, regardless of the original number's sign.

How do you calculate the absolute value of a number?

To calculate the absolute value of a number, you simply remove the negative sign (if any) and keep the positive value. For example, the absolute value of -3 is 3.

What is the difference between absolute value and magnitude?

Absolute value and magnitude are often used interchangeably, but they have slightly different meanings. Absolute value refers to the distance from zero, while magnitude refers to the size or amount of something. For example, the absolute value of -5 is 5, but the magnitude of -5 could also be interpreted as just 5.

Can absolute value be a decimal or fraction?

Yes, absolute value can be expressed as a decimal or fraction. For example, the absolute value of -0.5 is 0.5. In fact, any real number can have an absolute value.

What are some real-life applications of absolute value?

Absolute value is used in many real-life situations, such as calculating distance and speed, determining the error in measurements, and solving equations in physics and engineering. It can also be used in financial analysis to measure the deviation of stock prices from their average value.

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