Cogito
Grade 8 Math · Chapter 4 · Lesson 3
Equations with Brackets and Fractions
Clear the clutter first.
10 problems · about 19 minutes · 8.EE.C.7
What this lesson teaches
The child solves linear equations containing brackets and fractional coefficients.
- Expand brackets and clear fractions before collecting terms.
- Multiply every term on both sides, not only the fractional one.
- What is left is an ordinary linear equation.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — None, One, or Infinitely Many: 7x + 2 = 7x + 9. How many solutions?
Answer None.
Why No solution.
Review — 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.
3 problems5(x + 1) = 40. What is x?
Answer 7
Why x = 7.
2(x + 5) = 24. What is x?
Answer 7
Why x + 5 = 12.
x/5 = 4. What is x?
Answer 20
Why Multiply by 5.
Build It Up
The same ideas with more to keep track of.
2 problems3(x − 2) = 15. What is x?
Answer 7
Why x − 2 = 5.
x/4 + 1 = 6. What is x?
Answer 20
Why Multiply every term by 4.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Bracket: 4(x + 3) = 32. What is x?
Answer 5
Why x = 5.
The Fraction: x/2 + 3 = 9. What is x?
Answer 12
Why x = 12.