Cogito
Grade 7 Math · Chapter 6 · Lesson 2
Solving px + q = r
Undoing two operations in the right order.
10 problems · about 19 minutes · 7.EE.B.4
What this lesson teaches
The child solves two-step equations with rational coefficients.
- A two-step equation does two things to x.
- Undo them in reverse order: the last thing done is the first thing undone.
- Always check by putting the answer back in.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — 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.
Review — Why Two Negatives Make a Positive: (−6) × (−4) = ?
Answer 24
Why 24.
Warm Up
Straightforward practice. Get the method working first.
3 problems4x + 3 = 23. What is x?
Answer 5
Why x = 5.
5x + 2 = 17. What is x?
Answer 3
Why Take 2, then divide by 5.
3x − 4 = 11. What is x?
Answer 5
Why Add 4, then divide by 3.
Build It Up
The same ideas with more to keep track of.
2 problems2x + 9 = 3. What is x?
Answer -3
Why The answer is negative.
6x − 5 = 19. What is x?
Answer 4
Why Add 5, then divide by 6.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Equation: 2x + 6 = 18. What is x?
Answer 6
Why x = 6.
The Taxi Again: A taxi charges £3 plus £2 a mile. A fare of £17 covers how many miles?
Answer 7
Why 7 miles.