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Class 8 Linear Equations in One Variable — practice questions with answers

Linear Equations · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. Solve 5x + 3 = 2x + 18.
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Answer: A) 5
Move 2x left: 3x + 3 = 18 → 3x = 15 → x = 5.
2. Solve 4(2x − 3) = 20.
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Answer: C) 4
Distribute: 8x − 12 = 20 → 8x = 32 → x = 4.
3. Reena bought some pens at Rs 8 each and a notebook for Rs 30. She spent Rs 94 in all. How many pens did she buy?
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Answer: A) 8
Let the number of pens be x. 8x + 30 = 94 → 8x = 64 → x = 8 pens.
4. Two numbers are in the ratio 5 : 8. When 9 is added to each of them, the ratio becomes 2 : 3. Find the smaller number.
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Answer: D) 45
Let the numbers be 5x and 8x. Then → 3(5x + 9) = 2(8x + 9) → 15x + 27 = 16x + 18 → x = 9, so the smaller number is 5x = 45. Check: 54 : 81 = 2 : 3. The trap 9 is the value of x (not a number in the ratio) and 72 is the larger number.
5. Solve 5(x − 1) − 2(x + 3) = 2(x − 4) + 7.
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Answer: C) 10
Open every bracket: 5x − 5 − 2x − 6 = 2x − 8 + 7, so 3x − 11 = 2x − 1 and x = 10. Check: 5(9) − 2(13) = 45 − 26 = 19 and 2(6) + 7 = 19. Writing −2(x + 3) as −2x + 6 — failing to carry the minus onto the 3 — gives 3x + 1 = 2x − 1 and the trap −2.
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