One thing that I learned this week in Pre Calc 11 is how to solve absolute values. The definition of a absolute value is the principal square root of the square of the number. This definition explains that the number to the power of two square rooted is equal to the absolute value. The absolute value will always be a positive number also known as the “principal square root”. The absolute value is always a positive because when your solving for the “absolute value” your solving for the the “distance from 0” or “how far from 0” not the direction (positive or negative). For instance,

You can tell a number is a absolute value when it has absolute value bars around it, as seen above. It is important to remember these bars do not mean the same thing as parentheses or brackets. If you see absolute value bars with a equation inside you have to solve whats in-between the bars before solving.

Below is a example of a equation where you have to solve the absolute value before solving the equation. Follow the steps I took to solve the following example…