Algebra: Equations Basics

Equations

• 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)

Area of a Rectangle

• 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

Perimeter of a Rectangle

• 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

• 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

Area of a Rectangle

• 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

Perimeter of a Rectangle

• 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

Equations

• 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

• 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

Area of a Rectangle

• The area of a rectangle is found by multiplying the length by the width: A = lw
• Area is measured in square units (e.g. square meters, square feet)

Perimeter of a Rectangle

• 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)