Back in PreAlgebra we used a number of properties but never properly identified them. We called things 'inverse' or simply just used the properties but never justified our reasoning when solving for a variable. Now in Algebra, it is important to be able to justify WHY and HOW we get to each step. So, here are some of those properties you've been working with… 

Let's start off with a typical 2step linear equation like this one: I know you all know how to go about solving for x but let's see how you can use your deductive reasoning skills to actually justify the properties you use as you work through each step. Here we go! 

Step 1: Addition Property of Equality


Step 2: Division Property of Equality


I bet you are starting to get the idea behind these 'equality' properties now. Let's see if you are able to follow the steps in the next problem example. 

Step 1: Subtraction Property of Equality


Step 2: Multiplication Property of Equality


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