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Which statement about the equation is correct?

Class 8Linear Equations in One VariableLinear Equations
  • AIt is true for every value of (an identity)
  • BIt has exactly one solution
  • CIt has exactly two solutions
  • DIt has no solution

Step-by-Step Solution

Expanding the left side gives , identical to the right side, so any value of satisfies it.
Answer: A) It is true for every value of (an identity)

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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