Linear Equations in One Variable (Review) MCQs Quiz | Class 9
This quiz covers Unit II: Algebra for Class IX Mathematics (Code 041). It focuses on reviewing Linear Equations in One Variable, specifically solving simple linear equations, applying transposition rules, and verifying solutions through examples. Test your understanding, check your score, and download the solutions PDF for revision.
Topic Overview
A linear equation in one variable is an equation which can be written in the form ax + b = 0, where a and b are real numbers and a is not equal to zero. The variable appears with a power of exactly 1. Solving these equations involves finding the value of the variable that makes the equation true (LHS = RHS).
Key Concepts Review
1. Transposition Method: When moving a term from one side of the equation to the other, its sign changes.
- Plus (+) becomes Minus (-)
- Minus (-) becomes Plus (+)
- Multiplication (x) becomes Division (/)
- Division (/) becomes Multiplication (x)
Solving Steps
- Identify the variable term and constant terms.
- Use transposition to group variable terms on one side (usually LHS) and constants on the other (RHS).
- Simplify both sides.
- Isolate the variable by dividing or multiplying as required.
- Check the answer by substituting the value back into the original equation.
| Equation Type | Example | Step | Solution |
|---|---|---|---|
| Addition | x + 5 = 12 | Subtract 5 | x = 7 |
| Subtraction | y – 4 = 10 | Add 4 | y = 14 |
| Multiplication | 3z = 18 | Divide by 3 | z = 6 |
| Division | t / 2 = 5 | Multiply by 2 | t = 10 |
Quick Revision List
- An equation remains unchanged if the same number is added to or subtracted from both sides.
- An equation remains unchanged if both sides are multiplied or divided by the same non-zero number.
- Linear equations have exactly one unique solution.
Extra Practice Questions
- Solve for m: 7m + 19/2 = 13.
- Find x if 3x = 2x + 18.
- If you subtract 1/2 from a number and multiply the result by 1/2, you get 1/8. What is the number?
- Solve: (x – 5)/3 = (x – 3)/5.
- Two numbers are in the ratio 5:3. If they differ by 18, what are the numbers?
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