Linear Equations and Inequations
Solve rational-coefficient equations and inequations while preserving equivalence and representing solutions correctly.
How to study National 5 Mathematics
Secure one operational skill at a time, connect it to neighbouring techniques, then apply it in unfamiliar contexts with complete working and a checked conclusion.
Core concepts
Concept 1
Equivalent equations result from applying the same valid operation to both sides.
Exam cue: Remove brackets and denominators in a controlled order.
Concept 2
Fractions can be cleared using a common multiple before isolating the variable.
Exam cue: Collect variable terms and constants separately.
Concept 3
Multiplying or dividing an inequality by a negative number reverses the inequality sign.
Exam cue: Substitute a test value or check the boundary when validating an inequality.
Risk pitfalls and guardrails
Moving a term by changing its sign without preserving equality.
Guardrail: Check signs, brackets, restrictions, units, accuracy and whether the answer needs a reason.
Clearing only some denominators.
Guardrail: Check signs, brackets, restrictions, units, accuracy and whether the answer needs a reason.
Failing to reverse an inequality after division by a negative.
Guardrail: Check signs, brackets, restrictions, units, accuracy and whether the answer needs a reason.
Memory anchors
Equation balance
Apply the same operation to both sides.
Clear fractions
Multiply every term by a common denominator.
Collect terms
Variables on one side, constants on the other.
Inequality reversal
Reverse the sign when multiplying or dividing by a negative.
Boundary
The equality point separates possible solution regions.
Check
Substitute into the original equation or test the 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
Solve 3x + 5 = 20.
Solve 7 − 2x = 19.
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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