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Assertion (A): The equation has no solution. Reason (R): When the variable terms cancel, a false numerical statement remains. Which is correct?

Class 8Linear Equations in One VariableLinear Equations
  • ABoth A and R are true and R is the correct explanation of A
  • BBoth A and R are true but R is not the correct explanation of A
  • CA is true but R is false
  • DA is false but R is true

Step-by-Step Solution

Subtracting from both sides gives 3 = 5, which is false, so no value of works. R correctly explains why A is true.
Answer: A) Both A and R are true and R is the correct explanation of A

Key idea: The five-step recipe

For any linear equation in one variable, follow this order:

1. **Open brackets** if any (use distributive property).
2. **Clear fractions** by multiplying both sides by the LCM of all denominators.
3. **Move all variable terms to one side**, all constants to the other (transposition — flip signs).
4. **Combine like terms** on each side.
5. **Divide** both sides by the coefficient of the variable.

Then **verify** by substituting back into the original equation. Always.

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