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2. Elementary algebra - Wikipedia

   en.wikipedia.org/wiki/Elementary_algebra

   Two-dimensional plot (red curve) of the algebraic equation . Elementary algebra, also known as college algebra, [1] encompasses the basic concepts of algebra. It is often contrasted with arithmetic: arithmetic deals with specified numbers, [2] whilst algebra introduces variables (quantities without fixed values). [3]

3. Equation solving - Wikipedia

   en.wikipedia.org/wiki/Equation_solving

   Solving an equation symbolically means that expressions can be used for representing the solutions. For example, the equation x + y = 2x – 1 is solved for the unknown x by the expression x = y + 1, because substituting y + 1 for x in the equation results in (y + 1) + y = 2 (y + 1) – 1, a true statement. It is also possible to take the ...

4. Algebra - Wikipedia

   en.wikipedia.org/wiki/Algebra

   Solving an equation corresponds to adding and removing objects on both sides in such a way that the sides stay in balance until the only object remaining on one side is the object of unknown mass. The use of word problems is another tool to show how algebra is applied to real-life situations. For example, students may be presented with a ...

5. Collatz conjecture - Wikipedia

   en.wikipedia.org/wiki/Collatz_conjecture

   Closer to the Collatz problem is the following universally quantified problem: Given g, does the sequence of iterates g k (n) reach 1, for all n > 0? Modifying the condition in this way can make a problem either harder or easier to solve (intuitively, it is harder to justify a positive answer but might be easier to justify a negative one).

6. Extraneous and missing solutions - Wikipedia

   en.wikipedia.org/wiki/Extraneous_and_missing...

   Extraneous and missing solutions. In mathematics, an extraneous solution (or spurious solution) is one which emerges from the process of solving a problem but is not a valid solution to it. [1] A missing solution is a valid one which is lost during the solution process. Both situations frequently result from performing operations that are not ...

7. History of algebra - Wikipedia

   en.wikipedia.org/wiki/History_of_algebra

   Chiu-chang suan-shu or The Nine Chapters on the Mathematical Art, written around 250 BC, is one of the most influential of all Chinese math books and it is composed of some 246 problems. Chapter eight deals with solving determinate and indeterminate simultaneous linear equations using positive and negative numbers, with one problem dealing with ...