Absolute Value… makes everything positive, right? But, why?
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
Well, Absolute Value means a distance away from the origin (zero), and a distance is always positive!
Alright, that makes sense. But what about Absolute Value Equations and Inequalities?
So glad you asked!
Okay, so there is a big difference between taking the Absolute Value of a number versus taking the Absolute Value of a variable.
When you take the Absolute Value of a number, it just turns that number positive, like |3| = 3 and |-3|=3.
Easy, right?
But when you take the Absolute Value of a variable, you must account for both positive and negative direction.
For example, if we had |x|=5 that means we are either a distance of 5 units to the right of zero or we are a distance of 5 units to the left of zero, so we need to provide for both possibilities.
Absolute Value Equation
In this lesson we’re going to remind ourself of the most important, and often overlooked, step in solving Absolute Value Equations and Inequalities…
…getting the Absolute Value by itself before you solve!
But don’t worry, the process is straightforward, and simple to follow.
And, no matter if your solving an equation or a compound (conjunction) inequality, as Paul’s Online Notes accurately states, with less then (i.e., less “and”) or greater (i.e., great “or”) symbols, the steps are all the same!
Together we’re going to walk through 6 examples of how to solve Absolute Value Equations and 4 examples of how to solve Absolute Value Inequalities, all while expressing our answers in Interval Notation.
How to Solve Absolute Value Equations – Video
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