I don't think it 'began' as such - algebra is an abstract concept. You may as well ask how did painting begin, or how did singing begin.
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Algebra, just like the name itself, comes from the arabic countries in the middle east
Since "pre-" means before, then pre-algebra would be before algebra. Conversely, algebra would be after pre-algebra. Generally, the next class after a pre-algebra class would be Algebra I, followed by Algebra II.
Pre-algebra preps you for algebra.2nd answer:Pre-AP-algebra is the same as Algebra I. Both are way harder than pre- algebra.
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Elementary algebra