## Algebraisms 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