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I think this is what you're asking for.

3x=9 can be moved to be x=9/3

For a slope/intercept example:

3x-6y=-1 Subtract the 3x

-6y=-3x-1 Divide the negative 6 on y

y=1/2x+1/6 And there, (y=1/2x+1/6) is equal to (3x-6y=-1)

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Q: What is an example of an equivalent variable expression?
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