Linear Equations, Inequalities and Formulae
Solve linear equations and inequalities and rearrange formulae while preserving equivalence.
How to study for GCSE Mathematics
Use 601 original multiple-choice questions to learn connected methods, explain why they work, practise exact non-calculator execution and use a calculator strategically on designated papers.
Core concepts
Concept 1
Linear equations
Exam cue: Apply the same inverse operation to both sides, keeping grouped expressions intact; reverse an inequality only after multiplying or dividing by a negative.
Concept 2
Inequalities and number lines
Exam cue: Substitute a solution into the original equation or test values inside and outside an inequality region.
Concept 3
Changing the subject
Exam cue: Represent the information clearly, choose a justified method and communicate each step with correct notation and units.
Targeted study blocks
Tier coverage
Foundation core with Higher-tier extensions
Higher questions use more complex formulae, inequalities in two variables and algebraic structures with powers, fractions or repeated subjects.
Calculator structure
Prepare for calculator and non-calculator papers
Any part of a board's specification may be assessed on any paper. Non-calculator does not define a smaller syllabus; questions are designed so exact arithmetic and reasoning are feasible without a calculator.
Risk pitfalls and guardrails
Failing to reverse the inequality sign after division by a negative number.
Guardrail: Do not hide an invalid model behind arithmetic: check assumptions, signs, bounds, units, scale, required accuracy and the original question.
Giving an unsupported answer when the command requires working, proof, reasoning or interpretation.
Guardrail: Do not hide an invalid model behind arithmetic: check assumptions, signs, bounds, units, scale, required accuracy and the original question.
Assuming a topic belongs only to calculator or non-calculator papers; any specification content can be assessed on any paper.
Guardrail: Any part of a board's specification may be assessed on any paper. Non-calculator does not define a smaller syllabus; questions are designed so exact arithmetic and reasoning are feasible without a calculator.
Memory anchors
Equation balance
Apply the same valid operation to both sides.
Negative inequality rule
Reverse the inequality after multiplying or dividing by a negative.
Change the subject
Undo operations around the new subject in reverse order.
Linear Equations, Inequalities and Formulae: method
Apply the same inverse operation to both sides, keeping grouped expressions intact; reverse an inequality only after multiplying or dividing by a negative.
Linear Equations, Inequalities and Formulae: check
Substitute a solution into the original equation or test values inside and outside an inequality region.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
Foundation · AO1 technique · Non-calculator — Solve 7x−5=30.
Shared F/H · AO1 technique · Non-calculator — Solve 4(2x−3)=3x+13.
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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