Finding the Unknown

The simplest way to find a solution is to try numbers. x + 3 = 8: try 4, and 4 + 3 is 7, too small. Try 6, and 6 + 3 is 9, too big. Try 5, and both sides read 8. So x = 5.

That is called guess and check, and it is honest work: it uses exactly what an equation means. It also shows why an equation usually has just one solution: as the guess grows, the left side grows with it, and it passes 8 only once.

Guessing does not scale. For 7x - 4 = 3x + 8 or x/2 + x/3 = 10 you would be guessing all afternoon, and for an equation whose answer is 3/2 or -7 you might never land on it. From the next lesson on, you will find solutions by rewriting the equation, one legal step at a time, until it reads x = … by itself. This lesson, guess.