Fundamentals of Algebra and Trigonometry

📋 Course Outline

1. Linear Equations and Inequalities
2. Trigonometry
3. Measurement
4. Solving Linear Equations
5. Trigonometric Ratios
6. Units of Measurement

📖 1. Linear Equations and Inequalities

🔑 Key Concepts & Definitions

• Linear Equation: An algebraic equation of the first degree in which the highest power of the variable is one. It can be written in the form ax + b = 0, where a and b are constants, and a ≠ 0.
• Graphical Representation of Linear Equations: The visual depiction of a linear equation as a straight line on a coordinate plane, illustrating the solutions as points lying on that line.
• Properties of Inequalities: Characteristics such as the ability to multiply or divide both sides by a positive number without reversing the inequality sign, and reversing the sign when multiplying or dividing both sides by a negative number (authoritative (unknown)): fundamental rules for manipulating inequalities).
• Solving Linear Inequalities: The process of isolating the variable to find the range of values satisfying the inequality, often involving similar steps as solving equations but paying attention to the inequality sign, especially when multiplying or dividing by negatives.
• Applications of Linear Equations and Inequalities: Practical uses in fields like economics, engineering, and everyday problem-solving, such as budgeting, optimizing resources, and modeling real-world situations.