How many integers n satisfy |n − 3| + |n + 2| = 5?

Read |n − 3| as the distance from n to 3 and |n + 2| as the distance from n to −2. Those two marks are 5 apart, so the two distances add to exactly 5 precisely when n lies between them, endpoints included: −2 ≤ n ≤ 3. The integers are −2, −1, 0, 1, 2 and 3 — six of them. Step outside and the total grows: n = 4 gives 1 + 6 = 7. The trap 5 counts the gaps between the marks rather than the marks themselves — six numbers but only five steps — and 2 counts just the two endpoints, forgetting that everything in between works too.