Linear Equations in One Variable — Previous Year Questions (Class 8 Mathematics)
Solve linear equations with fractions, decimals, and variables on both sides. Master algebraic problem-solving techniques.
TL;DR: Solve linear equations with fractions, decimals, and variables on both sides. Master algebraic problem-solving techniques.
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Solve linear equations with fractions, decimals, and variables on both sides. Master algebraic problem-solving techniques.
Linear Equations in One Variable — Previous Year Questions with Solutions
Q (2023, 2 marks): Solve: 5x - 3 = 2x + 9
Answer: 5x - 3 = 2x + 9
Subtract 2x from both sides:
3x - 3 = 9
Add 3 to both sides:
3x = 12
Divide by 3:
x = 4
Verification: 5(4) - 3 = 20 - 3 = 17; 2(4) + 9 = 8 + 9 = 17 ✓
Q (2022, 3 marks): Solve: (x/2) + (x/3) = 10
Answer: x/2 + x/3 = 10
LCM of 2 and 3 = 6
(3x)/6 + (2x)/6 = 10
5x/6 = 10
5x = 60
x = 12
Verification: 12/2 + 12/3 = 6 + 4 = 10 ✓
Q (2023, 3 marks): Solve: 2(x - 1) = 3(x + 2)
Answer: 2(x - 1) = 3(x + 2)
Expand:
2x - 2 = 3x + 6
Subtract 2x from both sides:
-2 = x + 6
Subtract 6 from both sides:
x = -8
Verification: 2(-8-1) = 2(-9) = -18; 3(-8+2) = 3(-6) = -18 ✓
Q (2022, 3 marks): A number is multiplied by 3. The result is increased by 5. The final result is 26. Find the number.
Answer: Let the number be x.
Number multiplied by 3: 3x
Result increased by 5: 3x + 5
Final result: 3x + 5 = 26
3x = 21
x = 7
Verification: 3(7) + 5 = 21 + 5 = 26 ✓
Q (2023, 2 marks): Solve: 0.4x + 0.3 = 0.7
Answer: 0.4x + 0.3 = 0.7
Subtract 0.3 from both sides:
0.4x = 0.4
Divide by 0.4:
x = 1
Verification: 0.4(1) + 0.3 = 0.4 + 0.3 = 0.7 ✓
Q (2022, 3 marks): Solve: (3x - 5)/2 = (2x + 1)/3
Answer: Cross multiply:
3(3x - 5) = 2(2x + 1)
9x - 15 = 4x + 2
Subtract 4x from both sides:
5x - 15 = 2
Add 15:
5x = 17
x = 17/5 = 3.4
Frequently Asked Questions
What is transposition in equations?
Transposition is moving a term from one side of the equation to the other with the opposite operation. For example, in x + 5 = 12, we transpose 5 to get x = 12 - 5. This simplifies solving equations.
Why do we cross-multiply in fractional equations?
Cross-multiplication is a shortcut to eliminate fractions. In (a/b) = (c/d), cross-multiplying gives ad = bc, removing denominators and making the equation easier to solve.
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