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to be able to solve problems is the main purpose of studying algebra... :)
Algebra helps you solve real-world problems that you will face when you are on your own.
Language of Algebra
Yes, in a way. Algebra teaches you how to solve problems
It views problems in a different way starting in 8th grade usually
Algebra is used to solve simple problems involving know and unknown variables.
There are different ways of solving different problems, not a single way for all algebraic problems.
information, people
It was invented to systematically solve complicated logic/math problems.
Look at the example problems in any algebra book. Though some of the examples may be a bit far-fetched, many of the examples are similar to problems that scientists and engineers need to solve in the real world.
Algerbraic techniques can be applied to solve any sort of question! They also help you think in a way that allows you to solve many non-math problems.