Question on Isolating Variables

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SUMMARY

The discussion centers on isolating variables in equations with two variables, specifically addressing the confusion between canceling individual variables and treating them as like terms. Participants clarify that when combining terms such as ax + x, it simplifies to (a + 1)x, treating a + 1 as a single constant. The example provided, 3x - x, confirms that it simplifies to 2x, demonstrating the process of combining like terms effectively.

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Duckfan
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I was doing this last week and now I'm drawing blanks on an equation with 2 variables.

When you have a constant and a variable + a variable by itself, I forgot if I'm supposed to try to cancel the individual variable, or if I'm supposed to multiply/add it as a "like term".

I'm not giving equation yet (unless you really want me to) since I'm trying to solve this myself. And I'm beating up on myself too since I want to remember how to solve this. I'm just not remembering something as to what I isolate. I understand the rule on what you do on left side, you do on other. But the fact that I have 2 variables is confusing me-as to canceling the individual variable, or include it with the other term since it may be considered a like term.
Thank you.
 
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If you mean something like ax+ x, that is equal to (a+ 1)x and you can treat a+ 1 as a single constant.
 
HallsofIvy said:
If you mean something like ax+ x, that is equal to (a+ 1)x and you can treat a+ 1 as a single constant.

So if I had an equation or part of one eg, 3x - x, it would be 2x?
 
Yes. 3x - x = x + x + x - x = x + x = 2x.
 

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