Matchsticks, and what an equation is

Now find an unknown in a different setting. Here is a sequence of matchstick arrangements, one you studied in an earlier chapter, shown with their position numbers: 1, 2, 3, 4.

Jasmine decides to make an arrangement from this sequence using EXACTLY 99 sticks. What will its position number be?

To answer that, it helps to know the number of matchsticks at each position. The arrangement at position 1 has 2 × (1) + 1 = 3 matchsticks. At position 2 it has 2 × (2) + 1 = 5. At position 3 it has 2 × (3) + 1 = 7, and so on.

So the nth position has 2n + 1 matchsticks. Jasmine's question is now a question about a number: find the value of n for which 2n + 1 has the value 99. That is, 2n + 1 = 99.

A statement of EQUALITY between two algebraic expressions is called an EQUATION (in Hindi, समीकरण). Nowadays, when using symbols, we write an equation as two algebraic expressions with an equal sign '=' between them.

Here are more equations: 3x + 4 = 7, 20 = y − 3, a/3 = 50, 2z + 4 = 5z − 14. The part before the equal sign is the Left Hand Side (LHS) and the part after it is the Right Hand Side (RHS).

The process of finding the value or values of the letter-numbers for which the equality holds — for which the LHS becomes equal to the RHS — is called SOLVING the equation. As the matchstick problem shows, framing an equation using an unknown quantity as a letter-number can help us find its value. Worth asking: is it possible to make an arrangement in this sequence using exactly 200 sticks?