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S3 Maths: Linear Inequalities in One Unknown (Paper 4 (error clinic))
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 4 (error clinic))
Paper 4 (error clinic): 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 + 9 < 4.
- FoundationSolve the inequality 5x is at least 35.
- FoundationSolve the inequality x over 4 is at most minus 2.
- IntermediateSolve the inequality 8 – 3x > 2.
- IntermediateSolve the inequality 4x + 1 is at most 2x + 9.
- IntermediateSolve the inequality 2(x – 4) < 6.
- ChallengeSolve the inequality (3x – 2) over 2 > x + 1.
- ChallengeA book costs 45 dollars and postage is 12 dollars. With a budget of at most 300 dollars, what is the greatest number of books?
- ChallengeMei is 14 and her mother is 42. After at least how many years will the mother be less than twice as old as Mei?
- Error redoError clinic: a student solves 6 – 2x is at least 10 as x is at least minus 2. What is the correct solution?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | x < -5 | Subtract 9 from both sides to obtain x < -5. |
| 2 | x ≥ 7 | Divide both sides by 5 to obtain x at least 7. |
| 3 | x ≤ -8 | Multiply both sides by 4 to obtain x at most minus 8. |
| 4 | x < 2 | Subtract 8 to get -3x > -6, then divide by minus 3 and reverse to obtain x < 2. |
| 5 | x ≤ 4 | Subtract 2x and 1 to get 2x at most 8, so x at most 4. |
| 6 | x < 7 | Expand to 2x – 8 < 6, then add 8 and divide by 2 to obtain x < 7. |
| 7 | x > 4 | Multiply both sides by 2 to get 3x – 2 > 2x + 2, so x > 4. |
| 8 | 6 books | With n books, 45n + 12 is at most 300, so n is at most 6.4 and at most 6 books can be bought. |
| 9 | 15 years | After y years, 42 + y < 2(14 + y) gives y > 14, so at least 15 years are needed. |
| 10 | x ≤ -2 | Collect to get -2x at least 4, then divide by minus 2 and reverse to obtain x at most minus 2. |
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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