Exercise 2.3 — Variables on Both Sides

Exercise 2.3 — Equations with Variables on Both Sides

When a variable appears on both sides of an equation, you must collect all variable terms on one side before solving. Exercise 2.3 in Class 8 Mathematics develops this crucial skill and introduces equations that reduce to identities or contradictions — important for board examination questions.

Solving Strategy

• Transpose all variable terms to LHS and all constants to RHS — never try to solve without collecting like terms first.
• If the equation reduces to 0 = 0 after simplification, it is an identity — true for all values of x.
• If the equation reduces to a ≠ 0 (e.g. 3 = 0), it is a contradiction — no solution exists.
• Verify every solution by substituting into the original (not simplified) equation — simplification errors are caught this way.
• Cross-multiplication is the fastest method when the equation is in the form (ax+b)/(cx+d) = p/q.

Board Exam Weight

Equations with variables on both sides appear as 2-mark and 3-mark questions in CBSE, Telangana and Andhra Pradesh examinations. The identity and contradiction types appear as 1-mark MCQs asking you to identify the number of solutions. Master all three solution types to cover every variation the examiner might set.

How to Use This Lesson

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