As early as 3600 years ago, the mathematical problems written on papyrus by ancient Egyptians involved equations, that is, equations containing unknowns. Around 825 AD, Al Hualazimi, a mathematician in Central Asia, wrote a book called "Elimination and Return", focusing on solving equations.

The Chinese word "equation" comes from the ancient mathematical monograph "Nine Chapters of Arithmetic", the eighth volume of which is called "equation". "Fang" means juxtaposition, and "Cheng" is a vertical form with calculation.

Methods of solving equations:

(1) synthesis method

Firstly, the known number and unknown number in the application problem are listed as related algebraic expressions, and then the equivalent relationship between them is found out, and then the equation is listed. This is a thinking process from part to whole, and its thinking direction is from known to unknown.

(2) Analysis method

First, find out the equivalence relation, then according to the need of establishing equivalence relation, list the known numbers and set unknowns in the application problem into related algebraic expressions, and then list the equations. This is a thinking process from the whole to the part, and its thinking direction is from unknown to known.