Linear Equations in One Variable

A linear equation in one variable has the unknown to the first power only, and -- unlike an expression -- it has an equals sign, so it can be solved. The whole method rests on one idea CTET keeps testing through the 'balance' model: an equation is a balanced scale, and whatever you do to one side you must do to the other to keep it balanced. So we add, subtract, multiply or divide both sides by the same number to isolate the variable. The misconception the exam loves is the 'transposing without sign change' error -- a child moves a term across the equals sign but forgets that addition becomes subtraction. Another is dividing only one side. The balance model is the recommended teaching tool precisely because it makes the 'do the same to both sides' rule feel necessary rather than arbitrary. A useful pedagogy point: encourage children to verify the solution by substituting it back, which turns checking into part of the method instead of an afterthought. Always remember a linear equation in one variable has exactly one solution.

✅ Solved examples

✏️ Practice — try these, take hints as needed

📝 Topic test — 8 questions

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