Equation Study Guide

An equation is a mathematical statement that shows the equality of two expressions. It consists of two sides separated by an equals sign (=).

Types of Equations

There are different types of equations, including:

• Linear Equations: Equations of the form ax + b = c, where a, b, and c are constants and x is the variable.
• Quadratic Equations: Equations of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable.
• Exponential Equations: Equations involving exponential functions, such as 2^x = 16.
• Trigonometric Equations: Equations involving trigonometric functions, such as sin(x) = 0.5.

Solving Equations

To solve an equation, you aim to find the value of the variable that makes the equation true. This involves performing operations to isolate the variable on one side of the equation.

Steps to Solve an Equation

1. Combine Like Terms: Combine similar terms on each side of the equation.
2. Isolate the Variable: Use inverse operations (addition, subtraction, multiplication, division) to isolate the variable on one side of the equation.
3. Check Your Solution: Substitute the value found for the variable back into the original equation to ensure it satisfies the equality.

Equation Properties

Some important properties of equations include:

• Reflexive Property: For any real number a, a = a.
• Symmetric Property: If a = b, then b = a.
• Transitive Property: If a = b and b = c, then a = c.

Applications of Equations

Equations are used in various real-life scenarios, such as calculating distances, solving for unknown quantities in science and engineering, and modeling physical phenomena.