🔤 Algebra Basics (Variables & Equations)

Last Updated: 06-Sep-2025

Algebra is math with letters and symbols.
We use letters (like x, y, z) to represent unknown values.

👉 Example:

  • "I have some chocolates. If I add 5 more, I get 12."
  • Algebra form: x + 5 = 12
  • Here, x = unknown number of chocolates.

Variables

A variable is a symbol (usually a letter) that stands for a number.

  • Example: x = 10, y = 5

👉 Real life:

  • Taxi fare = ₹50 + ₹10 × kilometers
    • If km = 5 → fare = 50 + 10×5 = 100

Simple Equations

An equation shows that two things are equal.

👉 Example:

  • x + 3 = 7
    • To solve: subtract 3 from both sides → x = 4

Steps to Solve

  1. Keep variable on one side.
  2. Do same operation on both sides.
  3. Simplify to find value.

Examples

  1. Age Puzzle
    • Rahul is 5 years older than his sister.
    • If Rahul is 12, find sister’s age.
    • Equation: Sister = x → x + 5 = 12 → x = 7.
  2. Shopping
    • 2 pens cost ₹20.
    • Cost of 1 pen = 20 ÷ 2 = 10.
    • Equation: 2x = 20 → x = 10.

⚡ Quick Practice

  1. Solve: x + 7 = 15
  2. Solve: 2x = 18
  3. A number minus 5 is equal to 9. Find the number.
  4. A rectangle has length = x and width = 4. If perimeter = 18, find x.
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