As others have said, any time I figure out what gas will cost me to get to a specific place, or follow a recipe, I’m using algebra. Many people don’t realize that these kinds of calculations (which can usually be done in one’s head) are algebra, partly because they’re afraid of “school math” and I think also partly because they think of algebra as “a different language” as @Blueroses put it.
I don’t think of algebra as a different language… I just think of it as math. There are symbols, yes, but it doesn’t have a separate grammar or syntax; you can’t translate something into algebra that wasn’t already algebra (whether you knew it or not).
I think that enhancing the “other-ness” of math in this way just makes it more remote to people who are afraid of it. In this sense, I don’t know that it’s particularly useful to even give algebra a separate name from other kinds of math. It’s just a continuation of things one learned before algebra; it builds on arithmetic, and it will in turn be built on with calculus (which most of us do not use every day). But it’s not really “separate” from those kinds of math. All of the underlying rules and assumptions are the same.