Cogito
Grade 8 Math · Chapter 4 · Lesson 1
Variables on Both Sides
Gather them up first.
10 problems · about 19 minutes · 8.EE.C.7
What this lesson teaches
The child solves linear equations with variables on both sides.
- Gather all the variables onto one side.
- It then becomes a two-step equation.
- Check by working out both sides separately.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Comparing Lines in Different Forms: At x = 0, y = 8; at x = 5, y = 33. What is the slope?
Answer 5
Why 5.
Review — Unit Rate as Slope: A proportional line through (7, 28). What is its slope?
Answer 4
Why 4.
Warm Up
Straightforward practice. Get the method working first.
4 problemsSolve 7x + 3 = 4x + 18.
Answer 5
Why x = 5.
What is the first move with variables on both sides?
Answer Get all the variables onto one side.
Why Gather the variables first.
Solve 5x = 3x + 8.
Answer 4
Why Subtract 3x.
Solve 8x − 2 = 5x + 10.
Answer 4
Why Subtract 5x, add 2.
Build It Up
The same ideas with more to keep track of.
2 problemsSolve 4x + 6 = 2x + 14.
Answer 4
Why Subtract 2x.
Solve 9x − 5 = 6x + 7.
Answer 4
Why Subtract 6x, add 5.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Equation: Solve 6x + 1 = 4x + 11.
Answer 5
Why x = 5.
The Two Plans: Plan A costs 20 + 5 per month, plan B costs 10 + 7 per month. After how many months are they equal?
Answer 5 months
Why 5 months.