Basics

Algebra is a branch of mathematics that uses letters to represent numbers and solve problems.

The letters are called variables, because the numbers that the letters represent can vary.

The letters x and y are often used in algebra problems.

Common algebraic language includes linear expressions, linear equations, polynomial expressions, and polynomial equations.

In the algebraic equation y = 5x + 7

• x is a variable

• y is a variable

• 7 is a constant (does not change)

• 5 is a coefficient (a multiplier that does not change)

Linear Expression

Definition

An algebraic statement that performs functions of addition, subtraction, multiplication, and division. Exponents and roots are not allowed.

Example

x + y + 3

Linear Equation

Definition

A linear expression with an = sign.

Example

y = x + 3

Polynomial Expression

Definition

An algebraic statement that performs functions of addition, subtraction, multiplication, and division. Exponents and roots are allowed.

Example

x² + y + 3

Polynomial Equation

Definition

A polynomial expression with an = sign.

Example

y = x² + 3

Algebraic Word Problem

Definition

An algebraic problem requiring translation of Everyday Language into Math Action.

Example

The total cost *T* of renting a car is $35.00 times the number of days *d* the car is rented plus a one-time charge of $25.00.

Translation → T = 35d + 25