This week we learned about finding the absolute value of numbers.

“The absolute value of a real number is defined as the principal square root of the square of a number.”

If you wanted to find the absolute value of 5, you would express it as:

since and

Note: the absolute value will always be positive, so

These absolute values can also be used in more complicated expressions.

For example:

To do this you should treat the symbol for absolute value like brackets, and do everything inside first and then solve anything outside. Note that you cannot distribute into these like you can with brackets.

Now to solve:

Now when solving these, you actually can get a negative number as your answer, if your coefficient is negative.

Here’s some examples:

The answer was negative, since the coefficient was negative and when you multiply it with the positive absolute value, you end up with a negative answer. Here’s another example:

There can also be multiple sets of absolute values in expressions:

As you can see, there are many ways absolute values can be used in expressions/equations, but there are a few key points to always remember:

1. The absolute value of a number is always positive, but your answer could be negative if your coefficient is negative.
2. “The absolute value of a real number is defined as the principal square root of the square of a number.”
3. Absolute Values should be treated like brackets, and you should solve whats inside them before anything else is done, but you cannot distribute into them, think of the two lines as barriers you cannot cross until everything inside is solved.