Algebra is a branch of mathematics that uses letters and symbols to represent numbers and quantities in formulas and equations. This fundamental concept allows us to generalise mathematical ideas beyond simple arithmetic.
Introduction to Algebraic Representation
Algebra uses letters like , , to symbolize variables or unknown quantities, allowing for the formulation of equations and expressions that can universally apply beyond specific numerical instances.
- Variables: Symbols for unknown numbers.
- Constants: Known values.
- Coefficients: Numbers multiplying a variable.
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Algebraic Operations
Example 1: Solving an Equation
Problem: Find in .
Solution:
Example 2: Substitution
Problem: Given , evaluate .
Solution:
Algebraic Expressions
Example 3: Simplifying Expressions
Problem: Simplify .
Solution:
Representation in Equations
Example 4: Formulating Equations
Problem: Represent "a number plus three equals eleven" as an equation.
Solution:
Let the number be .
Solving Algebraic Equations
Example 5: Solving for a Variable
Problem: Solve .
Solution:
Practice Problems
1. Solve for :
Solution:
2. Given , find: .
Solution:
3. Simplify:
Solution: