Simple Equations

• Introduction to Equations

  • What is an Equation?
    • Condition on a variable
    • Contains an equality sign (=)
    • Has LHS (Left Hand Side) and RHS (Right Hand Side)
  • Balanced nature of an equation
    • LHS equals RHS for the solution

• Setting up an Equation

  • Translating verbal statements into mathematical forms
  • Example: "Sum of $x$ and $4$ is $9$" $\rightarrow$ $x + 4 = 9$
  • Example: "Two times $y$ minus $3$ is $7$" $\rightarrow$ $2y - 3 = 7$

• Solving an Equation (Finding the Solution)

  • Concept of a Root or Solution
    • Value of the variable that makes LHS = RHS
  • Methods of Solving
    • Trial and Error Method
      • Substitute random values until LHS = RHS
    • Systematic / Balancing Method
      • Performing the same mathematical operation on both sides
      • Operations allowed:
        • Add the same number to both sides
        • Subtract the same number from both sides
        • Multiply both sides by the same non-zero number
        • Divide both sides by the same non-zero number
    • Transposition Method
      • Moving a term from one side to the other
      • Changing the sign (positive becomes negative, multiplication becomes division)

• Applications of Simple Equations (Word Problems)

  • Steps to solve:
    • 1. Understand the problem and identify the unknown quantity
    • 2. Assign a variable (e.g., $x$) to the unknown
    • 3. Set up the equation based on given conditions
    • 4. Solve the equation for the variable
    • 5. Verify the answer