⚖️ Solving Linear Equations

What you’ll learn

1. Expressions & Equations VocabularyDistinguish expressions, equations, and inequalities, and identify terms, coefficients, factors, and constants within an expression.An expression is a phrase with no relation sign (3x + 5); an equation states equality (2x + 1 = 9); an inequality compares (x > 4). Within an expression, terms are the parts separated by + or −, a coefficient is the number multiplying a letter (the 3 in 3x), a constant is a term with no letter (5), and a factor is something that multiplies to build a term. The equals sign acts like a balance point, which underpins all equation solving.
2. Solving Linear EquationsSolve linear equations in one variable, including those needing bracket expansion, collecting like terms, and variables on both sides, using inverse operations.An equation must stay balanced, so whatever you do to one side you do to the other. Use inverse operations in reverse order: for 3x + 5 = 26, subtract 5 (3x = 21) then divide by 3 (x = 7). Expand brackets first — 2(x + 3) = 14 becomes 2x + 6 = 14 — and gather variable terms onto one side when the letter appears on both, as in 5x − 2 = 3x + 8 giving x = 5. Checking by substitution confirms the solution.
3. Factorising ExpressionsFactorise expressions by identifying the highest common factor of all terms and writing the expression as a product.Factorising reverses expanding: it writes an expression as a factor times a bracket. Find the highest common factor (HCF) of every term, then divide each term by it. For 6x + 9, the HCF of 6 and 9 is 3, so 6x + 9 = 3(2x + 3). You can always check by expanding the answer to see it returns the original expression.

Questions this course answers

Grounded in trusted sources

• BBC Bitesize — Maths (Key Stage 3)
• Khan Academy — Solving equations
• NRICH (University of Cambridge)
• Britannica

Every Wunder lesson is built from real, reputable sources — never invented.

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