Why are variables useful in algebra?

I feel the use of variables make it difficult for many people to understand because it is subconcious that math is numbers, not letters....

Thank you!

By using a variable, one may make use of a formula which is good for hundreds of situations where only the variable changes. If not for variables we would br forced to memorize each of those hundreds of situations rather than just the one.
I'm not sure I agree with you about why the use of variables makes it difficult for many people. I agree that it does make it difficult for many people; however, not for the reason you cite. I think it makes it difficult because using variables makes us think in the abstract whereas many people do better thinking in terms of the finite. If your "theory" is correct, then people would not have any trouble at all with fraction (all numbers) but I am told that fractions cause more trouble for more students than any other arithmetical operation, except, perhaps word problems.

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