Cogito
Grade 7 Math · Chapter 6 · Lesson 1
Two-Step Equations
Undo the operations in reverse order.
10 problems · about 18 minutes · 7.EE.B.4
What this lesson teaches
The child solves equations of the form px + q = r and p(x + q) = r.
- A two-step equation has two operations to undo.
- Undo them in reverse order.
- Check by substituting the answer back in.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — 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.
4 problemsSolve 7x − 2 = 33.
Answer 5
Why x = 5.
In 3x + 4 = 19, which do you undo first?
Answer The + 4, because it was done last.
Why Undo in reverse order.
Solve 2x + 7 = 19.
Answer 6
Why Subtract 7, divide by 2.
Solve 4x − 5 = 23.
Answer 7
Why Add 5, divide by 4.
Build It Up
The same ideas with more to keep track of.
2 problemsSolve 3(x + 2) = 21.
Answer 5
Why Divide by 3 first.
Solve 6x + 4 = 40.
Answer 6
Why Subtract 4, divide by 6.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Taxi: A taxi charges 3 plus 2 per mile, and the fare was 17. How many miles?
Answer 7 miles
Why 7 miles.
The Equation: Solve 5x − 3 = 22.
Answer 5
Why x = 5.