In this lesson, I have covered the Fundamental Principles and General Solving Strategies to solve Linear Equations. In the video, I go through some examples for clarity purposes.
1. Fundamental Principles
- The Goal: Isolate the variable on one side of the equation to find its value.
- Balance Rule: Whatever operation you perform on one side of the equals sign must be performed on the other to keep the equation balanced.
- Linear Definition: The exponent of the variable must be 1. These equations have at most one solution.
2. General Solving Strategies – Follow these steps in order to simplify and solve:
- Expand Brackets: Use the distributive property to remove parentheses.
- Clear Fractions: If the equation contains fractions, multiply every term by the Least Common Denominator (LCD) to work with whole numbers.
- Group Like Terms: Move all terms with variables to one side and all constant numbers to the other.
- Inverse Operations: Use addition/subtraction to move terms, then multiplication/division to isolate the variable.
Below is an exercise to practice what you have learned (or revised). Use the accompanying memorandum to assess your performance.
