Basic Algebra: An Introduction

Basic concepts of algebra of the real and complex numbers.

Algebra is a branch of mathematics that deals with symbols and the rules for manipulating those symbols. In elementary algebra, those symbols (today written as Latin and Greek letters) represent quantities without fixed values, known as variables. Just as sentences describe relationships between specific words, in algebra, equations describe relationships between variables.

Understanding Variables, Constants, Coefficients, and Terms

In algebra, we use letters to represent numbers. These letters are called variables because the numbers they represent can vary. For example, in the equation y = 2x + 3, x and y are variables.

A constant is a value that does not change. In the same equation, 2 and 3 are constants because they always represent the same values.

A coefficient is a number used to multiply a variable. In our example, 2 is the coefficient of x.

A term in an algebraic expression is an expression involving letters and/or numbers, multiplied together. In 2x + 3, 2x and 3 are terms.

Simplifying Algebraic Expressions

Simplifying an algebraic expression is a way to make a complex expression more understandable and easier to work with. Simplification might involve combining like terms (terms with the same variables and powers), using the distributive property, or other operations that don't change the value of the original expression.

For example, the expression 3x + 5x can be simplified to 8x by combining like terms.

Basic Operations with Algebraic Expressions

Just like numbers, algebraic expressions can be added, subtracted, multiplied, and divided.

• Addition: 3x + 2x = 5x
• Subtraction: 5x - 3x = 2x
• Multiplication: 3x * 2x = 6x^2
• Division: (6x^2) / (2x) = 3x

Introduction to Equations and Solving Simple Linear Equations

An equation is a statement that two expressions are equal. For example, 2x + 3 = 7 is an equation.

Solving an equation means finding the value of the variable that makes the equation true. For the equation 2x + 3 = 7, we can solve for x by subtracting 3 from both sides to get 2x = 4, and then dividing both sides by 2 to get x = 2.

Algebra is a powerful tool that allows us to solve complex problems by representing them in a simplified form. By understanding these basic concepts, you'll be well-prepared to explore more advanced algebraic concepts in the future.