Year 8 · Maths

Solving linear equations: Year 8 introduction

6 checked activities 4 video matches

Start here

Focus on solving linear equations step by step. Start with “Practise Solving Two-Stage Equations”, then explain the idea in your own words.

Understand the key idea

An equation stays true as long as you do the same thing to both sides. To solve for one unknown, undo the operations in reverse order: deal with addition and subtraction first, then multiplication and division. Always check by substituting your answer back into the original equation.

Common mix-up

Whatever you do to one side must be done to the whole of the other side. Subtracting 3 from 2x + 3 = 11 gives 2x = 8, not 2x = 11 − 3 applied to only part of the expression.

Try this first

Solve 3x + 4 = 19 and check the answer by substitution.
Solve an equation where the unknown appears on both sides.
Write an equation for "I think of a number, double it and add 5 to get 17".

Ask: How can you check an equation answer is right without asking anyone?

Year 8 learners practise solving linear equations step by step.

The activities include Practise Solving Two-Stage Equations, Simplify and Solve One-Stage Equations, Simplify and Solve Simple Equations, and related practice. The checked support below includes video, worksheet, teaching, lesson. Open a resource in its provider's website and choose the format that best helps the learner explain the idea independently.

Activities covered

Practise Solving Two-Stage Equations
Simplify and Solve One-Stage Equations
Simplify and Solve Simple Equations
Solve Equations with Brackets
Solve One-Stage Equations
Solve Two-Stage Equations

Learning path

These same-subject links were reviewed as the foundations for this topic and the learning it directly unlocks.

Learn this first

Year 7Use And Interpret Algebraic Notation
The unknown and operation conventions must be read correctly before an equation can be solved.
Year 8Simplify Algebraic Expressions To Maintain Equivalence
Collecting and simplifying equivalent expressions is needed before balancing an equation.

Where this leads next

Year 8Use Linear Equations Two Variables And Gradients
Extends a one-variable linear relationship to pairs of variables and straight-line graphs.
Year 8Interpret Mathematical Relationships Algebraically Geometrically
Connects the solved algebraic relationship to its geometric representation.

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Practise — questions or activities to try

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