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RD Sharma Solutions (Ex 2.3): Linear Equation in One Variable

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FAQs on RD Sharma Solutions (Ex 2.3): Linear Equation in One Variable

1. How do I know if an equation is linear in one variable?
Ans. A linear equation in one variable contains only one unknown letter (like x or y) with a power of 1, and no multiplication between variables. Examples include 2x + 5 = 13 or 3y - 7 = 8. The variable appears in a straight line relationship, never squared or under a root.
2. What's the difference between solving and checking a linear equation?
Ans. Solving means finding the value of the variable that makes the equation true through algebraic steps. Checking means substituting that solution back into the original equation to verify both sides are equal. For instance, if x = 4 solves 2x + 1 = 9, then 2(4) + 1 should equal 9 to confirm correctness.
3. Why do students get confused with transposing terms in linear equations?
Ans. Transposing requires changing the sign of a term when moving it across the equals sign-addition becomes subtraction and vice versa. Many students forget this sign change, leading to incorrect solutions. The rule works because whatever operation you do to one side must be done to the other to maintain balance.
4. Can a linear equation in one variable have no solution or infinite solutions?
Ans. Yes. If simplification leads to a false statement like 0 = 5, there's no solution. If it simplifies to a true statement like 0 = 0, there are infinite solutions. Most equations have exactly one solution, but these special cases occur with certain coefficient combinations in the given equation.
5. How do I handle linear equations with fractions and decimals in CBSE Class 8 exams?
Ans. Multiply the entire equation by the lowest common multiple (LCM) of all denominators to eliminate fractions, or by powers of 10 to remove decimals. This converts the equation into simpler whole numbers, making solving easier. After finding the solution, substitute back to ensure accuracy before finalising your answer.
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