Lesson 3 of 11
The same move with a letter inside
Show on a big screenEach house (a school team) sends n students, plus 4 teachers. Three houses go on a trip. How many people is that?
Step 1 of 4
- 3(n + 4). n has no value yet.
- 3 × n = 3n.
- 3 × 4 = 12.
- Opened: 3n + 12. At n = 5, both give 27.
The same move with a letter inside
The trip has 3n + 12 people.
A letter inside a bracket changes nothing about the move. The outside number multiplies every term, letter or not. So 3(n + 4) opens to 3n + 12, at every value of n.
Identity — a line that is true at every value you put in.
One match is not proof. A wrong line, 7n, also gives 21 at n = 3. At n = 4 it gives 28, but 3(n + 4) gives 24.
Slide n. Watch three answers.
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Try the lab to finish this lesson.