Class 8 Notes - Linear Equations in One Variable

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Linear Equations in One Variable

A linear equation in one variable is an equation that can be written in the form ax + b = c, where a, b, and c are numbers and x is the variable. The highest power of the variable is 1.

Key Concepts

  • Variable: A symbol (usually x) that represents an unknown number.
  • Equation: A mathematical statement that shows two expressions are equal.
  • Linear: The variable has no exponent other than 1.
  • Solution: The value of the variable that makes the equation true.

Examples of Linear Equations in One Variable

  • 2x + 5 = 11
  • y - 7 = 3
  • 4m = 20
  • z/3 + 2 = 6

How to Solve Linear Equations in One Variable

  1. Isolate the variable on one side of the equation using addition, subtraction, multiplication, or division.
  2. Simplify both sides as needed.
  3. Check your solution by substituting the value back into the original equation.

Step-by-Step Example

Example: Solve 3x - 4 = 11

  1. Add 4 to both sides: 3x - 4 + 4 = 11 + 4 ⇒ 3x = 15
  2. Divide both sides by 3: 3x/3 = 15/3 ⇒ x = 5
  3. Check: 3×5 - 4 = 15 - 4 = 11 ✔️

Word Problem Example

Problem: The sum of a number and 9 is 20. Find the number.

Solution:

  • Let the number be x.
  • x + 9 = 20
  • x = 20 - 9 = 11
  • Answer: The number is 11.

Practice Questions

  1. Solve: x + 7 = 15
  2. Solve: 5y = 35
  3. Solve: z/4 - 3 = 2
  4. Solve: 2m + 6 = 18
  5. If 3x = 21, what is x?

Common Mistakes

  • Not performing the same operation on both sides of the equation.
  • Forgetting to check the solution in the original equation.
  • Incorrectly adding or subtracting terms.

Summary

  • Linear equations in one variable have the form ax + b = c.
  • Solving means finding the value of the variable that makes the equation true.
  • Always check your answer by substituting it back into the original equation.