This week in math we learned about absolute values. In simple terms, an absolute value is the distance a number is from 0. The official definition is: the absolute value of a real number is defined as the principal square root of the square of a number. Any number that comes out of absolute value symbols will be positive. This is because the absolute value determines how many spaces a number is away from 0, so regardless of whether you are trying to find the absolute value of |-4| or |4|, it’ll always be a positive answer.
Absolute value symbols are grouping symbols which are similar to brackets except that you do not distribute with absolute value symbols. You always solve what is in the absolute value symbols first before dealing with any number outside of the symbols.
A few simple examples:
|-16| = 16
|9| = 9
|8-10| = |-2| = 2
-5|6-(-4)| = -5|6+4| = -5|10| = -50
When dealing with more complicated operations in absolute value equations, such as exponents and square roots, remember simple BEDMAS rules while taking into account the fact that you need to solve anything inside the absolute value symbols first, and anything outside the symbols afterwards.
I’ve included an example below of two more complex absolute value equations solved.