Class 8 Reducing to Simpler Form — 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:

\frac{x}{2}

= 5.

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Answer: D) 10

Multiply both sides by 2: x = 5 x 2 = 10.

2. Solve:

\frac{3 x}{5} = \frac{x + 4}{2}

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Answer: C) 20

Cross-multiply: 2(3x) = 5(x + 4), so 6x = 5x + 20, giving x = 20.

3. Solve:

\frac{x}{2} = \frac{x + 3}{4}

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Answer: D) 3

Cross-multiply: 4x = 2(x + 3), so 4x = 2x + 6, giving 2x = 6 and x = 3.

4. Solve:

\frac{3 x + 1}{16} + \frac{2 x - 3}{7} = \frac{x + 3}{8} + \frac{3 x - 1}{14}

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Answer: A) 5

LCM of 16, 7, 8, 14 is 112. Multiply: 7(3x + 1) + 16(2x - 3) = 14(x + 3) + 8(3x - 1). So 21x + 7 + 32x - 48 = 14x + 42 + 24x - 8, i.e. 53x - 41 = 38x + 34. Then 15x = 75, x = 5.

5. Solve:

\frac{6 x + 1}{3} + 1 = \frac{x - 3}{6}

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Answer: A) -1

Multiply by 6: 2(6x + 1) + 6 = (x - 3). So 12x + 2 + 6 = x - 3, i.e. 12x + 8 = x - 3. Then 11x = -11, x = -1.

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