Year 9 · Maths

Linear equations with brackets and fractions: Year 9 extension

3 checked activities 3 video matches

Start here

Focus on solving linear equations with unknowns on both sides. Start with “Find the Gradient of a Line Given Two Points”, then explain the idea in your own words.

Understand the key idea

Harder equations need a tidying step before balancing. Expand brackets first, and clear fractions by multiplying every term by the denominator. Then collect the unknowns on one side — usually the side with more of them, to keep the coefficient positive — and solve as normal.

Common mix-up

When clearing a fraction you must multiply every term in the equation, not only the fraction itself. Missing a term is the most common cause of a wrong answer here.

Try this first

Solve 2(x − 3) = 4x + 1 by expanding first.
Clear the fraction in (x + 1)/3 = 5 and solve.
Solve an equation with unknowns on both sides and negative coefficients.

Ask: When an equation has a fraction in it, what has to happen to every other term?

Year 9 learners practise solving linear equations with unknowns on both sides.

The activities include Find the Gradient of a Line Given Two Points, Solve Equations with Fractions, Solve Simple Linear Equations with Unknowns on Each Side. 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

Find the Gradient of a Line Given Two Points
Solve Equations with Fractions
Solve Simple Linear Equations with Unknowns on Each Side

Learning path

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

Learn this first

Year 8Simplify Algebraic Expressions To Maintain Equivalence
Expanding and collecting expressions is required before equations with brackets can be balanced.
Year 8Solving linear equations: Year 8 introduction
Secures inverse operations and balancing before brackets, fractions and unknowns on both sides.

Where this leads next

Year 9Use Linear Equations Two Variables And Gradients
Uses secure equation solving within linear relationships involving two variables.
Year 9Translate Situations Procedures Into Expressions Formulae And Graphs
Applies equation solving to relationships translated from real and mathematical situations.

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