They are extremely important because they allow you to solve many equations that have the same properties. they are like maps to find the right solution, without them, each equation would be individually figured out and no pattern would be established.
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No, geometry is more depth into algebra, with formulas and shapes. That's why algebra is a prerequisite
I suppose you mean "algebra". There are lots of formulas in algebra. Look up any introductory algebra school book.
Algebra exists to find solutions
Of course. Formulas are not encountered until the student progresses from arithmetic to algebra.
Islamic algebra is the same as regular algebra. just like Arabic numerals is the same as 1 2 3. why is algebra important today? there is no difference between these questions.