This set has twelve original questions, ordered from easier to harder, covering all five lessons in equations and formulas. Questions 1 to 4 are warm-ups, 5 to 8 add fractions and formulas, and 9 to 12 mix skills and ask you to check.
Work on paper, write every line, and only then open the answer. Use the non-calculator working trainer to test a fraction step, and log slips in the mistake log and retest queue.
Questions
1. Solve 3x + 5 = 20.
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Subtract 5: 3x = 15. Divide by 3: x = 5.
Check: 3 × 5 + 5 = 20. ✓
2. Solve 4(x − 3) = 20.
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Divide both sides by 4: x − 3 = 5. Add 3: x = 8. Or expand first: 4x − 12 = 20, so 4x = 32 and x = 8.
Check: 4 × (8 − 3) = 20. ✓
3. Solve 5x − 7 = 2x + 11.
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Subtract 2x: 3x − 7 = 11. Add 7: 3x = 18. So x = 6.
Check: 5 × 6 − 7 = 23 and 2 × 6 + 11 = 23. ✓
4. Solve 2(x + 4) + 3(x − 1) = 30.
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Expand: 2x + 8 + 3x − 3 = 30. Simplify: 5x + 5 = 30. So 5x = 25 and x = 5.
Check: 2 × 9 + 3 × 4 = 18 + 12 = 30. ✓
5. Solve x/3 + x/4 = 14.
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Multiply every term by 12: 4x + 3x = 168. So 7x = 168 and x = 24.
Check: 24/3 + 24/4 = 8 + 6 = 14. ✓
6. Solve (x + 5)/2 = (2x − 1)/3.
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Multiply both sides by 6: 3(x + 5) = 2(2x − 1). Expand: 3x + 15 = 4x − 2. Then 17 = x, so x = 17.
Check: (17 + 5)/2 = 11 and (34 − 1)/3 = 11. ✓
7. Solve 5 − 3(2x − 1) = 2(x + 4).
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Expand, noting the minus changes both signs: 5 − 6x + 3 = 2x + 8. Simplify: 8 − 6x = 2x + 8. Subtract 8 from both sides: −6x = 2x. So 0 = 8x and x = 0.
Check: 5 − 3(−1) = 8 and 2 × 4 = 8. ✓ An answer of zero is allowed.
8. Make x the subject of 3(x − a) = 2(x + b).
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Expand: 3x − 3a = 2x + 2b. Subtract 2x: x − 3a = 2b. Add 3a: x = 2b + 3a.
Test with a = 1 and b = 2: x = 7. Left side 3 × 6 = 18 and right side 2 × 9 = 18. ✓
9. Make c the subject of m = (2c + 1)/(c − 4).
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Multiply: m(c − 4) = 2c + 1. Expand: mc − 4m = 2c + 1. Collect c terms: mc − 2c = 1 + 4m. Factorise: c(m − 2) = 4m + 1. So c = (4m + 1)/(m − 2).
Test with m = 3: c = 13/1 = 13. Then (26 + 1)/(13 − 4) = 27/9 = 3. ✓
10. Taxi company A charges RM4 plus RM1.50 per km. Company B charges RM2 plus RM2 per km. For what distance do both charge the same, and what is the fare?
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Let d = distance in km. Then 4 + 1.5d = 2 + 2d. Subtract 1.5d and 2: 2 = 0.5d. So d = 4 km.
Fare: A gives 4 + 6 = RM10 and B gives 2 + 8 = RM10. Both charge RM10 at 4 km. ✓
11. A student solves 6 − 2(x + 1) = 3x + 9 and writes x = 1. Check whether this is right and, if not, find the correct value.
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Check in the original: left side 6 − 2 × 2 = 2. Right side 3 + 9 = 12. They differ, so x = 1 is wrong.
Solve: 6 − 2x − 2 = 3x + 9, so 4 − 2x = 3x + 9. Then −5 = 5x and x = −1.
Check: 6 − 2(0) = 6 and 3(−1) + 9 = 6. ✓
12. The formula C = 5(F − 32)/9 converts °F to °C. Make F the subject, then use your formula to convert 100 °C.
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Multiply by 9: 9C = 5(F − 32). Divide by 5: 9C/5 = F − 32. Add 32: F = 9C/5 + 32.
For C = 100: F = 900/5 + 32 = 180 + 32 = 212 °F.
Check in the original: 5(212 − 32)/9 = 5 × 180/9 = 100. ✓
If you got these wrong
- Questions 2, 4 and 7 (brackets, signs): return to solving with brackets. Draw an arrow from the outside number to every term inside.
- Questions 5 and 6 (fractions): return to equations containing fractions. Multiply every term, including whole numbers.
- Questions 8 and 9 (formulas): return to rearranging a formula. Write the operation on both sides, and factorise when the letter appears twice.
- Question 10 (words to equation): return to forming an equation from a verbal constraint. State what d means before writing anything.
- Questions 11 and 12 (checking): return to checking a solution. Always check in the original line.
- Questions 1 and 3 (basic balancing): revisit algebraic structure and practise inverse operations.
Once these feel steady, simultaneous relationships is the natural next module. If the same errors keep returning, online one-to-one Mathematics tuition gives you a teacher who reads your working and targets the habit, not just the question.