Mathematics which includes Algebra is considered "the mother of all science". Therefore it is used of course extensively in all higher mathematics and in all the sciences. It is possible to use some problem solving techniques that you learn in Algebra to solve proplems in real life even if you are not a scientist or mathematician.
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As by "who" i assume you mean what profession. Algebra is used a lot in banking, economics, and doctors who need formulas. But overall algebra is mostly used by college leveled advanced algebra teachers.
Algebra is used to help determine distances in time, or places
In algebra, one solution means that there is only one real value x that will satisfy its equation.
Many people learn algebra, and then never use it in their "real life". It's not that it COULDN'T be useful; but rather, that many people tend to forget how to use it. In some professions, you will DEFINITELY need algebra - as well as more advanced math.
Algebra is used in lots of differant ways in everyday life because it's maths.