Algebra

Algebraic Expressions: Variables, Terms, Coefficients and Like Terms

An expression combines numbers and variables (letters standing for numbers) with operations, like $3x + 5$. Like terms have exactly the same variable part and can be combined by adding their coefficients.

The Distributive Property: Expanding Brackets with the Area Model

The distributive property says $a(b + c) = ab + ac$: multiplying a sum means multiplying each part of it. It is how brackets are expanded, and, run backwards, how expressions are factorised.

How to Solve Linear Equations: The Balance Method

A linear equation like $3x - 4 = 11$ is solved by doing the same inverse operation to both sides until the variable is alone. Each step keeps the equation balanced, like a pair of scales.

Solving Linear Inequalities: Why the Sign Flips with Negatives

An inequality such as $x > 2$ describes a range of values rather than a single one. It is solved like an equation, except that multiplying or dividing both sides by a negative number reverses the inequality sign.

Interval Notation Explained: Brackets, Infinity and Unions

Interval notation writes a range of numbers using its endpoints: a square bracket includes an endpoint and a round bracket excludes it. So $-2 < x \le 5$ is written $(-2, 5]$.

Rearranging Formulae: How to Change the Subject of a Formula

Rearranging a formula means making a different letter its subject, the letter on its own on one side. You use the same balancing steps as solving an equation, treating the other letters as if they were numbers.