Algebra: The Art of Balancing
An equation is a statement that two things are equal. Solving an equation is like solving a mystery puzzle: you are given clues (numbers) and you have to find the missing piece (the variable x).
1. The Golden Rule of Algebra
"What you do to one side, you must do to the other."
Think of an equation like a balanced scale. If you add 5kg to the left side, the scale tips. You must add 5kg to the right side to bring it back to balance.
2. Isolation Strategies
The goal is to get 'x' alone. We do this by performing Inverse Operations (doing the opposite):
- If x is added by 5, subtract 5.
- If x is multiplied by 3, divide by 3.
- If x is squared, take the square root.
3. Types of Equations
- Linear: 3x + 5 = 11. (Answer is a single point).
- Quadratic: x² - 4 = 0. (Answer is usually two points, +2 and -2).
- Radical: sqrt(x) = 9. (Square both sides to solve).
4. Checking Your Work
The best part about algebra is that you can check if you are right. If you think x = 4, plug 4 back into the original equation. If both sides are equal, you are 100% correct. If not, check your math!