A generalization of arithmetic in which symbols are used to represent unknown quantities so that we can convert verbal expressions into more concise mathematical statements, thus making the thinking process as well as the solution process mechanized and automatic.
For example, to find out what number, plus a number that is one less, equals 11, a symbol "x" can be used to represent this unknown number. As a result, the above everyday language can be rewritten as "x, plus (x-1), equals 11." Further simplifying the expression produces the equation shown below:
x + (x-1) = 11
x + x-1 = 11
2x - 1 = 11
2x = 12
x = 6
You may wonder why we need to go through all this trouble, introducing a variable x, making an equation out of an ordinary statement, and then solving for x, when we can solve the original problem using simple arithmetic. The reason is that algebra is a higher level of arithmetic. The basic arithmetic we have learned is only sufficient to solve simple or small-scale problems. When the problems become more complex or grow into large-scale projects, we need more powerful tools to help us. This is where algebra shines. The advantage of using algebra will become more apparent when the problem grows more complex.