FAQs on linear equation in one variable |class 8th maths |ch-2 | ex -2.1 | Manjeet Singh| #linearequations

Question 1

1. How do I know if an equation is linear in one variable?

Accepted Answer

Ans. A linear equation in one variable contains only one unknown letter (like x or y) with no powers higher than 1, and no multiplication between variables. For example, 2x + 5 = 11 is linear, but x² + 3 = 7 is not. The variable appears only to the first power, making it solvable using basic arithmetic operations.

Question 2

2. What's the difference between solving linear equations and just simplifying expressions?

Accepted Answer

Ans. Solving a linear equation means finding the value of the variable that makes both sides equal-you're looking for a specific number. Simplifying an expression just rewrites it in shorter form without finding any particular value. When solving 3x - 4 = 11, you find x = 5; simplifying 3x - 4 gives no answer since there's no equals sign.

Question 3

3. Why do I have to do the same operation on both sides of an equation?

Accepted Answer

Ans. Both sides must remain equal to maintain the equation's balance. If you add, subtract, multiply, or divide only one side, the equality breaks. Imagine a balanced scale: adding weight to just one side tips it. Doing identical operations to both sides keeps the relationship true while isolating the variable to find its value.

Question 4

4. How do transposition and inverse operations help solve linear equations quickly?

Accepted Answer

Ans. Transposition moves terms across the equals sign by changing their sign-addition becomes subtraction and vice versa. Inverse operations undo each other (addition/subtraction, multiplication/division). Using these methods together speeds up solving: instead of lengthy step-by-step balancing, you directly shift terms. For 2x + 7 = 15, transpose 7 to get 2x = 8, then divide by 2 to find x = 4.

Question 5

5. Why do some linear equations have no solution or infinite solutions instead of just one answer?

Accepted Answer

Ans. Most linear equations in one variable have exactly one solution. However, if simplifying leads to a false statement like 0 = 5, there's no solution. If it reduces to a true statement like 0 = 0, infinite solutions exist-any number works. This occurs when the original equation is contradictory or represents the same line written differently, relevant for understanding equation behaviour in CBSE Class 8 mathematics.

linear equation in one variable -class 8th maths -ch-2 - ex -2.1 - Manjeet

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