Simple Equation

Definition of Simple Equation

• A simple equation is an expression that has a variable and an equality sign (=).
• Examples:
  • 2x = 10
  • 4x + 5 = 25
  • 10y - 20 = 50
• Here, two equations have the variable 'x' and the third one has 'y'.
• Understand the parts on the left-hand side and right-hand side of the equation.

Solution of an Equation

• The solution of an equation is the value that satisfies the equation.
• Examples:
  • Equation: x + 10 = 30
    • Solution: x = 20
  • Equation: 2x = 10
    • Solution: x = 5

Check the Solution

• Example:

  • Equation: x + 5 = 19
    • Given Value: x = 1
    • Check: 1 + 5 = 6 (which is not equal to 19)
    • Conclusion: x = 1, is not the solution.

• Another Example:

  • Equation: 7y + 2 = 16
    • Given Value: y = 2
    • Check: 7*2 + 2 = 16
    • Conclusion: y = 2, is the solution.

Set up an Equation

• Example:

  • Irfan has marbles 5 times Parmid plus 7 more.
    • Assume: M = Parmid's marbles.
    • Equation: 5M + 7 = 37

• Example:

  • Lakshmi's father's age is 49 years.
    • Equation: 3Y + 4 = 49
    • (Y = Lakshmi's age)

Solving the Equation

• Rules for solving the equation:
  • Pay attention to addition and subtraction processes.
  • Pay attention to multiplication and division processes.

Example:

• Equation: 3x + 6 = 24

  • Solution:
    • First, remove 6: 3x = 24 - 6 = 18
    • Then divide by 3: x = 18 / 3 = 6

• Another Example:

• Equation: 4x + 3 = 16

  • Solution:
    • First, remove 3: 4x = 16 - 3 = 13
    • Then divide by 4: x = 13 / 4 = 3.25

Application of Simple Equation

• Use: Solving puzzles.

• Example:

  • "Triple a number + 11 = 32"
  • Equation: 3x + 11 = 32
  • Solution: x = 7

• Another Example:

  • "Sachin scored twice as many runs as Rahul"
  • Equation: 2x + x = 198
  • Solution: Rahul = 66, Sachin = 132

---

These notes briefly present the definition, solution, equation setup, and solving process for simple equations. Additionally, examples of applications are provided.