Cogito
Grade 7 Math · Chapter 6 · Lesson 3
Solving p(x + q) = r
Two routes to the same answer.
10 problems · about 19 minutes · 7.EE.B.4, 7.EE.A.1
What this lesson teaches
The child solves equations with a bracket, by dividing first or expanding first.
- An equation with a bracket can be divided first or expanded first.
- Divide first when the division comes out clean.
- Both routes must give the same answer.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Solving px + q = r: 4x + 3 = 23. What is x?
Answer 5
Why x = 5.
Review — Two-Step Equations: Solve 7x − 2 = 33.
Answer 5
Why x = 5.
Review — Terminating and Repeating Decimals: Write 3/4 as a decimal.
Answer 0.75
Why 0.75.
Warm Up
Straightforward practice. Get the method working first.
3 problems6(x + 2) = 42. What is x?
Answer 5
Why x = 5.
3(x + 2) = 18. What is x?
Answer 4
Why x + 2 = 6.
5(x + 1) = 30. What is x?
Answer 5
Why x + 1 = 6.
Build It Up
The same ideas with more to keep track of.
2 problems2(x − 5) = 8. What is x?
Answer 9
Why x − 5 = 4.
Expand 3(x + 4). What is the number term?
Answer 12
Why 3 × 4.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Bracket: 2(x + 3) = 14. What is x?
Answer 4
Why x = 4.
The Other Route: 4(x − 1) = 20. What is x?
Answer 6
Why x = 6.