Cogito
Grade 8 Math · Chapter 4 · Lesson 2
None, One, or Infinitely Many
Not every equation has exactly one answer.
10 problems · about 18 minutes · 8.EE.C.7
What this lesson teaches
The child recognises equations with no solution and with infinitely many solutions.
- Most equations have one solution.
- A false leftover statement means no solution.
- A true leftover statement means infinitely many.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Variables on Both Sides: Solve 7x + 3 = 4x + 18.
Answer 5
Why x = 5.
Review — Comparing Lines in Different Forms: At x = 0, y = 8; at x = 5, y = 33. What is the slope?
Answer 5
Why 5.
Warm Up
Straightforward practice. Get the method working first.
4 problems7x + 2 = 7x + 9. How many solutions?
Answer None.
Why No solution.
The variable vanishes and leaves a true statement. What does that mean?
Answer Every value of x works.
Why Infinitely many solutions.
2x + 4 = 2x + 4. How many solutions?
Answer Infinitely many.
Why Always true.
6x + 1 = 6x + 8. How many solutions?
Answer None.
Why 1 = 8 is false.
Build It Up
The same ideas with more to keep track of.
2 problemsSolve 3x + 4 = x + 10.
Answer 3
Why One solution here.
4(x + 1) = 4x + 4. How many solutions?
Answer Infinitely many.
Why Expand the brackets.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Collapse: 3x + 2 = 3x + 9 leaves 2 = 9. How many solutions?
Answer 0
Why None.
The Identity: 5(x + 2) = 5x + 10 leaves 10 = 10. Does every value of x work?
Answer Yes. Infinitely many solutions.
Why Every value works.