MHB Question on Isolating Variables

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The discussion revolves around isolating variables in equations with two variables. The participant is confused about whether to cancel an individual variable or treat it as a like term when performing operations. Clarification is provided that terms like ax + x can be combined to (a + 1)x, treating a + 1 as a single constant. An example is given where 3x - x simplifies to 2x, confirming the correct approach. Understanding how to combine like terms is essential for solving equations with multiple variables effectively.
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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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