Linear inequalities for Singapore O-Level G3 Math
An inequality describes a range of values. Adding or subtracting the same amount preserves order. Multiplying or dividing by a negative reverses order: 2 < 5 becomes −2 > −5 when both sides are multiplied by −1.
What this guide covers
Linear inequalities in one variable and solutions on a number line. Two-variable shaded regions are outside this guide.
Syllabus reference: 2026 Mathematics 4052, N7, page 7. These are Mentora search groupings, not new official syllabus categories.
The content in this guide was also checked against 2027 G3 Mathematics K310, N7, page 7 on 2026-09-12. This is subject-content alignment, not a claim of complete syllabus coverage.
Use this guide for revision
What questions usually test
- Solve a linear inequality in one variable and state the full range of values.
- Reverse the sign only when multiplying or dividing both sides by a negative.
- Represent strict or inclusive bounds with the right number-line endpoint.
How to revise linear inequalities
Step 1
Isolate the variable
Treat both sides evenly and keep the inequality direction visible.
Step 2
Draw the boundary
Use an open endpoint for < or > and a filled endpoint for ≤ or ≥.
Step 3
Test a value
Substitute one value from the shaded side and check the boundary separately.
What changes the inequality sign?
- Add or subtract
- Adding or subtracting the same value on both sides keeps the inequality direction.
- Multiply or divide by a positive
- The direction stays the same.
- Multiply or divide by a negative
- Reverse the inequality direction. For example, −2x ≥ 8 becomes x ≤ −4.
- Draw the number line
- Use an open endpoint for < or >, and a filled endpoint for ≤ or ≥. Shade only the values that satisfy the final inequality.
Worked example
Solve 7 − 3x < 16 and show the solution on a number line.
Subtract 7: −3x < 9. Divide by −3 and reverse the sign: x > −3. Use an open circle at −3 and shade to the right. Test x = 0: 7 < 16 is true; the endpoint x = −3 gives 16 < 16, which is false.
Try three practice checks
Attempt each on paper before revealing the worked answer. These sample particular skills; they do not diagnose the whole topic or establish mastery.
Check 1
Solve 4x + 1 ≤ 13.
Show worked answer
Subtract 1 and divide by positive 4: x ≤ 3. Use a filled endpoint at 3 and shade left.
Check 2
Solve −2x ≥ 8.
Show worked answer
Divide by −2, reversing the sign: x ≤ −4. Use a filled endpoint at −4 and shade left. At x = −5, 10 ≥ 8 is true.
Check 3
List the integers satisfying −1 < 2x + 1 ≤ 7.
Show worked answer
Subtract 1 throughout: −2 < 2x ≤ 6. Divide by 2: −1 < x ≤ 3. The integers are 0, 1, 2, 3; −1 is excluded.
Common mistakes to watch for
- Reverse the sign for multiplication or division by a negative, not simply whenever a negative number appears.
- Open endpoints mean strict < or >; filled endpoints include equality.
- Do not list only integer solutions unless the question restricts the variable to integers.
If one of these occurs, compare the relevant step with the worked example, then try a different question before drawing conclusions.
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Published by Mentora · Sources checked 12 Sept 2026
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Original public examples and answers were checked with automated mathematical/editorial QA. No individual author, human reviewer or independent expert review is recorded.