Absolute value of real numbers

In summary, the absolute value of a real number is its distance from 0 on a number line and is always a positive value. To calculate the absolute value of a real number, simply remove the negative sign (if there is one). Absolute value is used in math to represent distance and magnitude without regard to direction, and it can also simplify mathematical expressions and equations. While absolute value and magnitude are often used interchangeably, they have slightly different meanings. Absolute value cannot be negative as it represents distance on a number line.
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Reals $x,\,y$ and $z$ satisfies $3x+2y+z=1$. For relatively prime positive integers $p$ and $q$, let the maximum of $\dfrac{1}{1+|x|}+\dfrac{1}{1+|y|}+\dfrac{1}{1+|z|}$ be $\dfrac{q}{p}$. Find $p+q$.
 
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Related to Absolute value of real numbers

What is the absolute value of a real number?

The absolute value of a real number is its distance from 0 on the number line. It is always a positive value, regardless of whether the original number is positive or negative.

How is the absolute value of a real number represented?

The absolute value of a real number is typically represented with vertical bars surrounding the number. For example, the absolute value of -5 would be written as |-5|.

What is the relationship between absolute value and distance?

The absolute value of a real number is the same as its distance from 0 on the number line. This means that the absolute value of a negative number is the same as the distance between that number and 0.

How is the absolute value of a real number calculated?

To calculate the absolute value of a real number, you simply remove the negative sign (if there is one). For example, the absolute value of -8 would be 8.

What is the difference between absolute value and magnitude?

Absolute value and magnitude are often used interchangeably, but there is a subtle difference. Magnitude refers to the size or length of a vector, while absolute value refers to the distance from 0 on the number line. In other words, magnitude is a concept used in vector algebra, while absolute value is used in real numbers.

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