Algebra: Equations Basics

Study Notes

An equation is a statement that says two expressions are equal
It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS)
The goal is to solve for the variable (usually represented by a letter) by isolating it on one side of the equation
Types of equations:
- Linear equations: degree of the variable is 1 (e.g., 2x + 3 = 5)
- Quadratic equations: degree of the variable is 2 (e.g., x^2 + 4x + 4 = 0)
- Simple equations: can be solved in one step (e.g., 2x = 6)

The area of a rectangle is found by multiplying the length and width
Formula: Area = Length x Width
Unit of measurement: square units (e.g., square meters, square feet)
Example: If a rectangle has a length of 5cm and a width of 3cm, the area is 5cm x 3cm = 15cm^2

The perimeter of a rectangle is the distance around the outside of the shape
Formula: Perimeter = 2(Length + Width)
Unit of measurement: linear units (e.g., meters, feet)
Example: If a rectangle has a length of 5cm and a width of 3cm, the perimeter is 2(5cm + 3cm) = 2 x 8cm = 16cm

Equations are statements that equate two expressions
They consist of a left-hand side (LHS) and a right-hand side (RHS)
The goal is to isolate the variable on one side of the equation
There are different types of equations, including:
- Linear equations with a degree of 1
- Quadratic equations with a degree of 2
- Simple equations solvable in one step

The area of a rectangle is found by multiplying the length and width
The formula for the area is: Area = Length x Width
The unit of measurement for area is square units (e.g., square meters, square feet)
Example: a rectangle with a length of 5cm and a width of 3cm has an area of 5cm x 3cm = 15cm^2

The perimeter of a rectangle is the distance around the outside of the shape
The formula for the perimeter is: Perimeter = 2(Length + Width)
The unit of measurement for perimeter is linear units (e.g., meters, feet)
Example: a rectangle with a length of 5cm and a width of 3cm has a perimeter of 2(5cm + 3cm) = 2 x 8cm = 16cm

An equation is a statement that says two expressions are equal
Equations can be linear or non-linear, with linear equations having the form: ax + by = c
Solving an equation involves three steps: simplifying both sides, isolating the variable, and checking the solution

Graphing is a way to visualize equations on a coordinate plane with two axes: x-axis (horizontal) and y-axis (vertical)
A point on the plane is represented by an ordered pair (x, y)
Graphing involves creating a table of values, plotting points, and connecting them to form a curve or line

The perimeter of a rectangle is the distance around the outside of the rectangle
Perimeter is calculated using the formula: P = 2l + 2w
Perimeter is measured in units (e.g. meters, feet)