Algebra is a branch of mathematics that deals with symbols and letters (called variables) to represent numbers and quantities. Instead of always using specific numbers, algebra allows us to write general rules and formulas that can solve many problems at once.
1. Basic Idea
- In arithmetic, you work with specific numbers:
Example: ( 5 + 3 = 8 ) - In algebra, you use letters to represent unknowns:
Example: ( x + 3 = 8 ) ( x = 5 )
Here, (x) is a variablea symbol that can stand for an unknown number.
2. Common Elements of Algebra
- Variables letters like (x, y, z) representing unknown numbers.
- Constants numbers that stay the same (like 3, 7, 10).
- Expressions combinations of variables and constants using operations:
Example: (2x + 5) - Equations statements that two expressions are equal:
Example: (2x + 5 = 11)
3. Why Algebra Is Useful
- It helps solve unknown problems (like finding how much something costs).
- It lets us generalize rules (formulas for area, distance, speed, etc.).
- It is the foundation for advanced math: geometry, calculus, physics, and engineering.
4. Example
Problem: You have some apples. You buy 3 more, and now you have 10. How many did you start with?
Algebra solution:
[
x + 3 = 10
]
[
x = 10 – 3
]
[
x = 7
]
So, you started with 7 apples.
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