Algebra is a fundamental branch of mathematics that deals with symbols, variables, and mathematical operations. Unlike arithmetic which works with specific numbers, algebra uses letters like x, y, and a to represent unknown values. This allows us to solve problems and express general mathematical relationships.
In algebra, we work with two main types of mathematical objects: variables and constants. Variables are symbols like x, y, or z that represent unknown or changing values. They can take on different numbers depending on the problem. Constants, on the other hand, are fixed numbers that never change, such as 5, negative 3, pi, or e.
Algebraic expressions are mathematical phrases that combine variables, constants, and operations. For example, three x plus five is a linear expression, two x squared minus four x plus one is a quadratic expression, and x plus two over x minus one is a rational expression. These expressions form the building blocks of algebraic equations.
Solving linear equations involves using inverse operations to isolate the variable. Let's solve two x plus three equals eleven. First, we subtract three from both sides to get two x equals eight. Then we divide both sides by two to get x equals four. This systematic approach works for any linear equation.
Algebra has countless applications in the real world. We use it to calculate distances using the formula distance equals rate times time, to find areas like the area of a circle using pi r squared, in finance for compound interest calculations, and in physics with Newton's second law force equals mass times acceleration. Algebra provides the mathematical foundation for solving practical problems in science, engineering, economics, and everyday life.