Understanding Linear Equations in One Variable
Linear equations in one variable are equations that can be expressed in the form ax + b = 0, where 'a' and 'b' are constants, and 'x' is the variable.
Key Characteristics:
- Linear: The equation represents a straight line when graphed on a coordinate plane.
- One Variable: There is only one variable, making it simpler to solve.
Importance in Mathematics:
- Foundation: They form the basis for more complex algebraic concepts.
- Real-world Applications: Used in various fields like economics, physics, and engineering to model relationships.
Steps to Solve Linear Equations:
1. Isolate the Variable: Rearrange the equation to get the variable 'x' on one side.
2. Simplify: Combine like terms to simplify the equation.
3. Check Your Solution: Substitute the value of 'x' back into the original equation to verify.
Example Problem:
- Solve the equation 2x + 5 = 15.
- Step 1: Subtract 5 from both sides: 2x = 10.
- Step 2: Divide both sides by 2: x = 5.
- Step 3: Verification: Substitute x = 5 into the original equation to confirm.
NCERT Solutions (Part-1):
NCERT solutions provide a comprehensive approach to solving linear equations in one variable. They include:
- Detailed Steps: Each solution breaks down the process for clarity.
- Practice Problems: A variety of problems help reinforce concepts.
Understanding and mastering linear equations in one variable is essential for students, laying a strong foundation for future math learning.