Collecting like terms

A shop sells kaya buns. Every box holds n buns. n stands for the number of buns in 1 box. Nobody has counted them. One morning, 6 boxes come in, and 12 more buns. Then 5 boxes are sold, and 8 of the loose buns. Write how many buns are left, in the simplest form. Let's write the morning down as it happened. 6 boxes came in. That's 6 n. Then 12 more buns. Plus 12. 5 boxes were sold. Minus 5 n. And 8 loose buns. Minus 8. Every one of those is right. But you still can't see what's left on the counter. To see it, we put the same kinds together. Boxes with boxes. Loose buns with loose buns. And a term takes its sign with it. The minus in front of 5 n belongs to the 5 n. So the line becomes 6 n minus 5 n plus 12 minus 8. Now match them up. 6 boxes against 5. That leaves 1 box. We write that box as n, not 1 n. When there's just one of something, the 1 isn't written. Now the buns. 12 minus 8. That leaves 4. And that's as far as it goes. The n and the 4 can't join up. A box and a bun are not the same kind of thing, so n plus 4 stays as n plus 4. So the whole morning comes down to this. n plus 4. 1 box, and 4 buns. Now you can see what's on the counter. No other terms can be combined together, and that's what simplest form means.

Your turn. Sometimes a question comes with no story at all. Just a line like this, and one word. Simplify 15 plus 7 n plus 9 minus 3 n minus 4 plus 2. Here n could stand for anything at all. It doesn't change what you do. Try it first. Pause if you like. We look at the letters first. 7 n minus 3 n. That's 4 n. Then the plain numbers. 15 plus 9 minus 4 plus 2. That's 22. So the simplest form is 4 n plus 22. Letters with letters. Numbers with numbers. Every minus stays with its own term. And when nothing else can join, you're done.