# Why we use letters Arithmetic uses only numbers: `3 + 5 = 8`. **Algebra** lets a letter stand for a number we do not know yet — or a number that can change. > Everyday: “A ticket costs ₹x.” We do not know x yet, but we can still write `2x` for two tickets. ## Why bother? - One rule can work for **many** numbers - We can find a hidden number from clues - Science, coding, and money all use this idea ## Not a new alphabet test `x` is not a secret English word. It is a **box** that holds a number. `x + 4 = 10` means: *some number, plus 4, makes 10.* ## Slow down — what is actually new? You already know 3 + 5 = 8. That is arithmetic: every number is visible. Algebra starts when we say: “I do not know the number yet, but I can still write about it.” That is not a trick. Shopkeepers do it (“price = ₹x”), scientists do it (“time = t seconds”), and programmers do it (`score = score + 1`). ### Three jobs a letter can do 1. **Unknown** — we will find it: `x + 4 = 10` 2. **Changing quantity** — it can be many values: `cost = 40n` 3. **General number** — a rule that is always true: `n + n = 2n` ### Read it as a sentence `2x + 5` → “two times the mystery number, then plus five.” If you can say the expression in words, you already understand it. ### Try this out loud Point at any price tag in your kitchen. Say: “If the price is x, three of them cost 3x.” That is algebra in the real world.