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S3 Maths: Linear Inequalities in One Unknown (Paper 1 (basics))
Tutor Prep Guide · Inequality rules, adding and subtracting both sides, multiplying and dividing by positive or negative numbers, reversing the sign, removing brackets and denominators, integer solutions
S3 Maths: Linear Inequalities in One Unknown (Paper 1 (basics))
Paper 1 (basics): ten questions on linear inequalities in one unknown, with answers and notes.
Direct answers Level: S3 maths; format: solving inequalities, inequality rules, brackets and denominators, integer solution problems.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 20 |
| Difficulty mix | Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: S3 Maths: Linear Inequalities in One Unknown |
| Level | S3 |
02 Questions (10 items)
- FoundationSolve the inequality x + 5 > 8.
- FoundationSolve the inequality x – 4 is at most 2.
- FoundationSolve the inequality 4x < 20.
- IntermediateSolve the inequality 2x + 3 is at least 11.
- IntermediateSolve the inequality 3x – 5 < 7.
- IntermediateSolve the inequality -2x > 8.
- ChallengeSolve the inequality 5x – 7 < 2x + 8.
- ChallengeSolve the inequality 4(x – 2) is at least 12.
- ChallengeThree times a number plus 4 is greater than 19. Find the smallest integer value of the number.
- Error redoError clinic: a student solves minus x > 4 as x > -4. What is the correct solution?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | x > 3 | Subtract 5 from both sides to obtain x > 3. |
| 2 | x ≤ 6 | Add 4 to both sides to obtain x at most 6. |
| 3 | x < 5 | Divide both sides by 4, which keeps the sign, to obtain x < 5. |
| 4 | x ≥ 4 | Subtract 3 to get 2x at least 8, then divide by 2 to obtain x at least 4. |
| 5 | x < 4 | Add 5 to get 3x < 12, then divide by 3 to obtain x < 4. |
| 6 | x < -4 | Divide both sides by minus 2 and reverse the sign, giving x < -4. |
| 7 | x < 5 | Subtract 2x and add 7 to get 3x < 15, so x < 5. |
| 8 | x ≥ 5 | Expand to 4x – 8 at least 12, then add 8 and divide by 4 to obtain x at least 5. |
| 9 | 6 | With 3x + 4 > 19 we get x > 5, so the smallest integer is 6. |
| 10 | x < -4 | Divide both sides by minus 1 and reverse the sign, so the answer is x < -4. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
Adding or subtracting the same number keeps the inequality sign, while multiplying or dividing by a negative number reverses it. For at least or at most, set up the inequality first and then test the boundary value.Tutor Registration →
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