Year 7 Algebra Notes

Introduction to Algebra

  • Definition: Algebra is a branch of mathematics that uses letters and symbols to represent numbers in equations and expressions.

Key Concepts

  • Variables: Letters that represent unknown values (e.g., x, y).

  • Constants: Fixed values (e.g., 5, -3).

  • Expressions: Combinations of variables and constants (e.g., 3x + 4).

  • Equations: Statements that two expressions are equal (e.g., 2x + 3 = 7).

Basic Operations

  1. Addition: Combine like terms (e.g., 2x + 3x = 5x).

  2. Subtraction: Combine like terms (e.g., 5x - 2x = 3x).

  3. Multiplication: Use the distributive property (e.g., 2(x + 3) = 2x + 6).

  4. Division: Divide terms (e.g., ( \frac{4x}{2} = 2x )).

Solving Equations

  • To solve for a variable, isolate it on one side of the equation.

  • Example: Solve for x in the equation 2x + 3 = 7.

    • Subtract 3 from both sides: 2x = 4.

    • Divide by 2: x = 2.

Order of Operations

  • When simplifying expressions, follow the order of operations:

    1. Parentheses

    2. Exponents

    3. Multiplication and Division (from left to right)

    4. Addition and Subtraction (from left to right)

Types of Algebraic Expressions

  • Monomials: A single term (e.g., 3x).

  • Binomials: Two terms (e.g., x + 2).

  • Polynomials: Multiple terms (e.g., x^2 + 3x + 2).

Practice Problems

  1. Simplify the expression: 5x + 3x - 2.

  2. Solve for x: 3x - 4 = 11.

  3. Expand: 2(x + 5).

  4. What is the value of x in the equation 4x + 9 = 25?