Algebra Fundamentals

A variable is a symbol, usually a letter like x or y, that represents an unknown or changeable quantity in a mathematical expression or equation.

An algebraic expression is a combination of variables, constants, and operations (such as addition, subtraction, multiplication, and division) without an equals sign. For example, 3x + 5 is an algebraic expression.

A coefficient is the numerical factor multiplied by a variable in a term. In the term 7x, the coefficient is 7.

A constant is a fixed numerical value that does not change. In the expression 2x + 9, the constant is 9.

To evaluate an expression means to substitute specific values for the variables and then simplify using the order of operations to obtain a numerical result.

Like terms are terms that have the same variable raised to the same power. For example, 3x² and −5x² are like terms because they both contain x². Like terms can be combined by adding or subtracting their coefficients.

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by each term inside a set of parentheses.

Distribute first: 8x − 12 + 5x. Then combine like terms: 13x − 12.

A linear equation is an equation in which the highest power of the variable is 1. Its graph is a straight line. The general form is ax + b = 0.

Subtract 7 from both sides: 3x = 15. Divide both sides by 3: x = 5.

Distribute: 5x − 10 = 3x + 4. Subtract 3x: 2x − 10 = 4. Add 10: 2x = 14. Divide by 2: x = 7.

An equation has no solution when simplifying leads to a contradiction such as 0 = 5. This means no value of the variable can make the equation true.