Algebra Basics

Study Notes

Variable: a symbol that represents a value that can change
Constant: a value that does not change
Term: a number, variable, or product of numbers and variables
Expression: a group of terms combined using addition, subtraction, multiplication, and division
Equation: a statement that says two expressions are equal

Addition and Subtraction Properties: add or subtract the same value to both sides of an equation to isolate a variable
Multiplication and Division Properties: multiply or divide both sides of an equation by the same non-zero value to isolate a variable

A variable represents a value that can change, often denoted by a letter or symbol.
A constant is a value that does not change, often represented by a number.
A term is a number, variable, or product of numbers and variables, such as 2x or 3y.
An expression is a group of terms combined using addition, subtraction, multiplication, and division, such as 2x + 3y.
An equation is a statement that says two expressions are equal, such as 2x + 3y = 5.

The Distributive Property allows you to multiply a single number or variable to each term inside the parentheses, such as a(b + c) = ab + ac.
The Commutative Property states that the order of numbers or variables does not change the result, such as a + b = b + a.
The Associative Property states that the order in which you perform operations does not change the result, such as (a + b) + c = a + (b + c).

The Addition and Subtraction Properties allow you to add or subtract the same value to both sides of an equation to isolate a variable.
The Multiplication and Division Properties allow you to multiply or divide both sides of an equation by the same non-zero value to isolate a variable.

A point is a location in space, represented by a set of coordinates (x, y, z) that define its position.
A line is a set of points extending infinitely in two directions, and can be defined by two points or an equation.
A plane is a flat surface extending infinitely in all directions, and can be defined by three points or an equation.

An acute angle is an angle less than 90 degrees, such as 30 degrees or 45 degrees.
A right angle is an angle equal to 90 degrees, formed by two perpendicular lines.
An obtuse angle is an angle greater than 90 degrees, but less than 180 degrees.
A straight angle is an angle equal to 180 degrees, formed by two lines that lie in the same plane.
The perimeter of a shape is the distance around it, and can be calculated by adding the lengths of its sides.
The area of a shape is the amount of space inside it, and can be calculated using various formulas.

A triangle is a polygon with three sides and three angles, and can be classified as acute, right, or obtuse.
A quadrilateral is a polygon with four sides and four angles, and can be classified as a rectangle, square, or trapezoid.
A polygon is a shape with at least three sides and angles, and can be classified as a triangle, quadrilateral, or other shape.
A circle is a set of points equidistant from a central point (center), and can be defined by its center and radius.