IP EMaths Notes (Upper Sec, Year 3-4): 04) Linear Equations and Inequalities

Study guide08 Nov 2025, 00:00 ZUpdated 30 Nov 2025

Isolate variables cleanly and represent inequality solutions in interval or graphical form.

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Q: What does IP EMaths Notes (Upper Sec, Year 3-4): 04) Linear Equations and Inequalities cover?
A: Isolate variables cleanly and represent inequality solutions in interval or graphical form.

The core idea is simple: Do the same operation to every side, and flip an inequality when multiplying or dividing by a negative.

Use it as a working check: Linear questions are mostly bookkeeping. Clear fractions, collect like terms, isolate the variable, then show the final answer as a value, interval, or shaded number line.

Then go one layer deeper: Use the examples to see how equations and inequalities differ: equations pin down exact values, while inequalities describe ranges that may or may not overlap.

Linear manipulations appear everywhere - simultaneous systems, variation models, and coordinate geometry. Practice consistent isolation and be fluent with inequality notation.

Keep the full topic roadmap handy via our IP Maths tuition hub so you can jump into related drills, quizzes, or diagnostics as you move through these notes.

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These notes align with SEAB GCE O-Level Mathematics (4052) content used in IP programmes (exams from 2026).

Status: SEAB O-Level Mathematics 4052 syllabus (exams from 2026) checked 2025-11-30 - scope unchanged; remains the reference for these notes.

Key reminders

Keep the equation balanced: whatever operation you apply to one side must be applied to the other.
When multiplying or dividing an inequality by a negative number, reverse the inequality symbol.
Present solution sets with interval notation or on a number line where appropriate.

Equation-or-inequality checkpoint

Before solving, decide whether the question wants one exact value, a range, an overlap of ranges, or a list of allowed integers.

Question cue	First move	Output form	Common trap
Contains $=$

Reviewed by

Marcus Pang·Managing Director (Maths)

Operation applied to every side	Flip the sign?	Why	Common trap
Add or subtract the same expression	No	The order of the two sides is preserved.	Flipping just because a negative term appears in the line.
Multiply or divide by a positive number	No	Positive scaling keeps the order the same.	Forgetting that division by $2$ , $0.5$ , or another positive value keeps the symbol direction.
Multiply or divide by a negative number	Yes	Negative scaling reverses the order on the number line.	Solving $-3x < 12$ as $x < -4$ instead of $x > -4$ .
Simplify first, then divide by the coefficient	Depends on the coefficient	Decide at the final division step.	Seeing a negative bracket earlier and flipping before the actual division step.

IP EMaths Notes (Upper Sec, Year 3-4): 04) Linear Equations and Inequalities

Key reminders

Equation-or-inequality checkpoint

Sources

Inequality sign-flip checkpoint

Worked example - Solve and interpret

Worked example - Solve a linear equation with fractions

Worked example - Solve a compound inequality

Worked example - Intersection of two independent inequalities

Worked example - Three-condition inequality system

Practice Quiz

Try this

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