Year 7 Algebra Guide
This guide covers the fundamentals of Year 7 Algebra, including key terminology, rules,
worked examples, and practice problems. It progresses from basic concepts to harder
equations to help you build confidence and mastery in algebra.
1. Key Terminology
Variable: A letter that represents an unknown number (e.g., x, y).
Coefficient: The number multiplying a variable (e.g., in 5x, the coefficient is 5).
Constant: A fixed number on its own (e.g., 7 in x + 7).
Expression: A combination of numbers, variables, and operations (e.g., 3x + 2).
Equation: A statement showing two expressions are equal (e.g., 2x + 3 = 7).
Like Terms: Terms with the same variable and power (e.g., 3x and 5x).
Simplify: Combine like terms to make an expression shorter.
Expand: Multiply out brackets (e.g., 2(x + 3) = 2x + 6).
Factorise: Put an expression into brackets (e.g., 2x + 6 = 2(x + 3)).
Subject of a formula: Rearranging an equation so a variable is on its own (e.g., making x
= ...).
2. Basic Algebra Skills
Start with simple steps in algebra. These are the foundation before solving equations.
• Simplifying: Combine like terms.
Example: 3x + 4x = 7x
• Expanding brackets: Multiply everything inside.
Example: 2(x + 5) = 2x + 10
• Factorising: Reverse of expanding.
Example: 6x + 12 = 6(x + 2)
3. Solving Equations
Equations are solved by keeping them balanced. Whatever you do to one side, do to the
other.
Example: Solve 2x + 3 = 9
Step 1: Subtract 3 from both sides → 2x = 6
This guide covers the fundamentals of Year 7 Algebra, including key terminology, rules,
worked examples, and practice problems. It progresses from basic concepts to harder
equations to help you build confidence and mastery in algebra.
1. Key Terminology
Variable: A letter that represents an unknown number (e.g., x, y).
Coefficient: The number multiplying a variable (e.g., in 5x, the coefficient is 5).
Constant: A fixed number on its own (e.g., 7 in x + 7).
Expression: A combination of numbers, variables, and operations (e.g., 3x + 2).
Equation: A statement showing two expressions are equal (e.g., 2x + 3 = 7).
Like Terms: Terms with the same variable and power (e.g., 3x and 5x).
Simplify: Combine like terms to make an expression shorter.
Expand: Multiply out brackets (e.g., 2(x + 3) = 2x + 6).
Factorise: Put an expression into brackets (e.g., 2x + 6 = 2(x + 3)).
Subject of a formula: Rearranging an equation so a variable is on its own (e.g., making x
= ...).
2. Basic Algebra Skills
Start with simple steps in algebra. These are the foundation before solving equations.
• Simplifying: Combine like terms.
Example: 3x + 4x = 7x
• Expanding brackets: Multiply everything inside.
Example: 2(x + 5) = 2x + 10
• Factorising: Reverse of expanding.
Example: 6x + 12 = 6(x + 2)
3. Solving Equations
Equations are solved by keeping them balanced. Whatever you do to one side, do to the
other.
Example: Solve 2x + 3 = 9
Step 1: Subtract 3 from both sides → 2x = 6
