Singapore Math linear inequalities guide for families and teachers outside Singapore. What students learn in Secondary 3 or 4 about solving inequalities in one variable and showing the solution on a number line.
An inequality describes a range of values, not a single answer.
Solving one is almost the same as solving an equation, with one important difference.
In Singapore Mathematics, students use the inequality symbols from Secondary 1. In Secondary 3 or 4, G3 students solve linear inequalities in one variable and represent the solution on the number line. MOE’s teaching syllabus includes simultaneous inequalities at this stage.
Additional Mathematics then extends the idea to quadratic inequalities.
This guide is useful for families and teachers who want to:
- understand what Singapore expects for inequalities, and how G2 and G3 differ;
- teach inequalities as a careful extension of equations;
- prepare a student who is moving into a Singapore secondary school; or
- support a student using Singapore Math materials in another country.
Quick facts
Level: Secondary 3 or 4 (G3 Mathematics); G2 Mathematics has only simple forms
Strand: Number and Algebra (N7 Equations and inequalities)
Official source: MOE Secondary Mathematics Syllabuses (2020 Secondary 1 cohort onwards) and SEAB G3 Mathematics syllabus K310 for the SEC from 2027 (O-Level 4052 in 2026)
Comes after: Linear Equations and Integers and Real Numbers
Leads to: Quadratic Functions and Inequalities in Additional Mathematics
What Linear Inequalities Mean in Singapore Mathematics
An inequality compares two quantities using <, >, ≤ or ≥.
x > 3 means x is greater than 3. x ≤ −1 means x is less than or equal to −1.
A linear inequality such as 2x + 5 < 11 has infinitely many solutions: every number less than 3.
Solving uses the same steps as an equation. The one difference is that multiplying or dividing both sides by a negative number reverses the inequality sign.
For example, 2 < 5, but −2 > −5. The site’s page Why Does the Inequality Sign Reverse When We Multiply by a Negative Number? explains the reason in detail.
Solutions are shown on a number line. An open circle means the end value is not included. A filled circle means it is included.
Where Linear Inequalities Sit in the Singapore Syllabus
In MOE’s teaching syllabus for G3 Mathematics, inequalities build over several years.
| Level | What G3 students learn |
|---|---|
| Secondary 1 | Ordering numbers on the number line; use of the symbols <, >, ≤ and ≥ |
| Secondary 2 | Simple inequalities |
| Secondary 3 or 4 | Solving linear inequalities in one variable and representing the solution on the number line |
| Additional Mathematics | Solving quadratic inequalities and representing the solution on the number line |
SEAB’s G3 Mathematics syllabus (K310) states the content as “solving linear inequalities in one variable, and representing the solution on the number line”.
MOE’s teaching syllabus adds “(including simultaneous inequalities)”. These are two inequalities that must both be true, such as 2x − 1 < 7 and 3x + 2 ≥ −4.
The G2 difference. G2 Mathematics has only “solving simple inequalities in the form ax ≤ b, ax ≥ b, ax < b and ax > b where a and b are integers”. Simultaneous inequalities are G3-only.
How Singapore Teaches Linear Inequalities
1. Read the symbols aloud
Students say “x is greater than or equal to 4” for x ≥ 4, and learn that it means the same as 4 ≤ x.
2. Show solutions on a number line
Use an open circle for < and >, a filled circle for ≤ and ≥, and an arrow showing the direction of the solution.
3. Solve like an equation
Add or subtract on both sides, and multiply or divide both sides by positive numbers, exactly as with equations.
4. Reverse the sign for negatives
When multiplying or dividing both sides by a negative number, reverse the inequality sign. Testing with numbers shows why.
5. Combine two inequalities
For simultaneous inequalities, solve each one, then find the values that satisfy both. Drawing both on the same number line makes the overlap clear.
6. Answer the question asked
Some questions ask for the largest integer, the smallest integer or all the integer values that satisfy an inequality.
Testing one value inside the solution and one outside it is the quickest check a student can learn.
Worked Examples
Solving with a negative coefficient
Question: Solve 5 − 3x ≤ 17 and show the solution on a number line.
Step 1. Subtract 5 from both sides: −3x ≤ 12.
Step 2. Divide both sides by −3 and reverse the sign: x ≥ −4.
Step 3. On the number line, draw a filled circle at −4 with an arrow pointing to the right.
Check: x = 0 should work: 5 − 0 = 5, and 5 ≤ 17. x = −5 should fail: 5 + 15 = 20, and 20 is not ≤ 17.
Simultaneous inequalities (MOE teaching syllabus)
Question: Find the integer values of x that satisfy both 2x − 1 < 7 and 3x + 2 ≥ −4.
Step 1. 2x − 1 < 7 gives 2x < 8, so x < 4.
Step 2. 3x + 2 ≥ −4 gives 3x ≥ −6, so x ≥ −2.
Step 3. Both are true when −2 ≤ x < 4.
Step 4. The integer values are −2, −1, 0, 1, 2 and 3.
Check: x = 3 gives 5 < 7 and 11 ≥ −4, so it works. x = 4 gives 7 < 7, which is false, so 4 is excluded.
Common Mistakes
- Forgetting to reverse the sign. −2x > 6 becomes x > −3. Fix: dividing by −2 reverses the sign, so x < −3. Test x = −4: −2 × (−4) = 8, and 8 > 6.
- Reversing the sign when it should stay. In 2x − 5 > −11, students reverse the sign because a negative number appears. Fix: only multiplying or dividing by a negative reverses it. Here 2x > −6, so x > −3.
- Using the wrong circle. Fix: filled for ≤ and ≥, open for < and >.
- Including the boundary in an integer list. For x < 4, students list 4. Fix: test the boundary value in the original inequality.
- Writing an equation answer. Students solve 3x + 1 > 10 and write x = 3. Fix: the answer is a range, x > 3.
- Taking either inequality instead of both. Fix: for simultaneous inequalities, the solution is the overlap, where both are true at once.
Teaching Linear Inequalities Outside Singapore
A few points are worth knowing when you use Singapore materials elsewhere.
- Symbols. The SEAB syllabus prints the “or equal to” signs as ⩽ and ⩾. They mean the same as ≤ and ≥.
- Representation. The G3 syllabus wording asks for the solution on the number line, so that is the form to practise. Some curricula also use interval notation.
- Timing. Singapore places solving linear inequalities in Secondary 3 or 4, well after linear equations in Secondary 1. The Singapore Math Placement guide helps you judge readiness.
- Subject level. If your child may join a Singapore school, note the G2 and G3 difference. G2 has only simple forms such as ax ≤ b, while G3 includes the full one-variable work.
- Calculators. An approved calculator may be used in both G3 Mathematics papers, but the reasoning here is algebraic and the working should be shown.
How to Practise Linear Inequalities at Home
A short, regular routine works better than one long weekend session.
- Read five inequalities aloud, then read each one from the other side.
- Draw three solutions on a number line, mixing open and filled circles.
- Solve two inequalities with positive coefficients and one with a negative coefficient.
- Test each answer with one value inside and one value outside the solution.
- Solve one pair of simultaneous inequalities and list the integer solutions.
- Once a week, write one real situation as an inequality, such as “at most 40 people” as n ≤ 40.
Ten to fifteen minutes is enough when the work is focused.
Try These
- Solve 4x + 3 > 19.
- Solve 7 − 2x ≥ 1.
- Find the largest integer x such that 3(x − 2) < 10.
- Solve −1 < 2x + 3 ≤ 9 and list the integer solutions.
Answers
- x > 4. Subtract 3, then divide both sides by 4.
- x ≤ 3. Subtract 7 to get −2x ≥ −6, then divide by −2 and reverse the sign.
- 5. The inequality gives 3x − 6 < 10, so 3x < 16 and x < 16/3, which is about 5.33. The largest integer is 5.
- −2 < x ≤ 3, with integer solutions −1, 0, 1, 2 and 3. Subtract 3 throughout to get −4 < 2x ≤ 6, then divide by 2.
What Comes Next
- In Additional Mathematics, Quadratic Functions and Inequalities covers solving quadratic inequalities and representing the solution on the number line.
- A sketch of a quadratic graph is a common way to see where a quadratic expression is positive or negative, which builds on Quadratic Graphs.
A student who tests a value inside and outside every solution is well prepared for these.
Frequently Asked Questions
When do Singapore students learn linear inequalities?
The symbols are used from Secondary 1. Solving linear inequalities in one variable and showing the solution on a number line is Secondary 3 or 4 content in G3 Mathematics.
Why does the inequality sign reverse with a negative number?
Multiplying by a negative number reverses the order of numbers: 2 < 5, but −2 > −5. The diagnostic page on this rule explains it fully.
Are simultaneous inequalities in the syllabus?
MOE’s teaching syllabus for G3 includes them. SEAB’s G3 Mathematics syllabus states the content as “solving linear inequalities in one variable, and representing the solution on the number line”. Simultaneous inequalities are not part of G2 Mathematics.
What is the difference between G2 and G3 here?
G2 has only simple inequalities of the form ax ≤ b, ax ≥ b, ax < b and ax > b, where a and b are integers. G3 solves linear inequalities in one variable more generally and, in MOE’s teaching syllabus, simultaneous inequalities.
Do students need interval notation?
The G3 syllabus wording asks for the solution on the number line, so that is the representation to practise for Singapore work.
Where do quadratic inequalities come in?
In Additional Mathematics, which includes “solving quadratic inequalities, and representing the solution on the number line”.
Helpful Reading
- Singapore Mathematics | International Edition: Linear Equations
- Singapore Mathematics | International Edition: Integers and Real Numbers
- Singapore Mathematics | International Edition: Quadratic Functions and Inequalities
- Why Does the Inequality Sign Reverse When We Multiply by a Negative Number?
- What Changes from Secondary 2 to Secondary 3 Mathematics?
- Why Are Negative Numbers So Easy to Get Wrong in Mathematics?
- How to Make Sense of the SEC G3 Mathematics Syllabus
- MOE Secondary Mathematics Syllabuses (2020)
- SEAB G3 Mathematics Syllabus K310
Linear Inequalities in Singapore Mathematics
An inequality is a range, not a point.
Solve it like an equation.
Reverse the sign only for a negative multiplier or divisor.
Choose the circle with care.
Test one value inside and one outside.
Taught this way, inequalities stop being a list of exceptions.
They become a careful extension of equations, and that care carries a student into Additional Mathematics.
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Singapore Mathematics | International Edition is a Bukit Timah Tutor guide series for families and teachers outside Singapore. It is not a textbook and is not affiliated with MOE, SEAB or any publisher. Syllabus details were checked against MOE and SEAB documents in October 2026. Always confirm current requirements with your school.
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