The thing that we did most, and that I remember most in the first semester is isolating the variable. The first time we did that, was when we tried to solve one-sided equations for a variable. For example, 4=5x-1. In that case x=1, and that can be found by reversing all arithmetical actions taken in the original equation until the variable is by itself. First, you would add one to both sides. The negative and positive ones would cancel each other out, and leave you with 4+1=5x. Then you would simplify the equation by combining like terms, or putting together the things that are alike, which would give you 5=5x. When two numbers or variables are right next to each other with a sign, the action taken is multiplication, and to undo multiplication, division is used. You would then be left with 1.

The next time we used "isolate the variable" was in two-sided equations. For example, 3x+1=2x+2. To solve that problem you would do the same, but need to subtract the variables as well. So, 2x would be subtracted from each side, along with 1. x=1 is what would be left, and that would be the answer.
 


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