How to Use This Absolute Value Calculator?

The absolute value is a math operation applied to real numbers that is defined as follows:

• For a real number \(x\), if \(x\) is positive (or zero), the absolute value of \(x\) is just \(x\)
• On the other hand, if \(x\) is negative, the absolute value of \(x\) is \(-x\)

What is absolute value symbol?

Mathematically speaking, the most common symbol used for absolute value is \(| x |\), which represents the absolute value of a given number \(x\). But that is not always the case, as some calculators may use their own specific notation, such as \(abs(x)\), which is also commonly used.

Absolute Value Equations

One of the most common applications of absolute value, aside from simply calculating absolute value of numbers is its use on equations. For example

\( |x - 1 | = 3\)

corresponds to a absolute value equation, because there is an equation that needs to be solved for \(x\), and there is an absolute value involved in there. This kind of equation could be harder to deal with because of the need of dealing with the absolute value correctly.

Examples of absolute value calculations

For example:

\[ |3| = 3\]

because 3 is positive. On the other hand,

\[ |-5| = -(-5) = (-1)\cdot(-5) = 5\]

because -5 is negative, and the absolute value of a negative number is computed by multiplying the number, in this case \(-5\), by \(-1\)