Grade 9 · Math · Unit 5 of 9
Multi-Step Equations
Brackets, fractions and both sides
What your child practises
Solving linear equations with brackets, fractions and variables on both sides, checking solutions, and turning word problems into equations.
Nunavut Curriculum approved guide: Alberta Mathematics K–9 (2007), Patterns and Relations · solving linear equations and single-variable inequalities
How we explain it
Children can open this short lesson before they practise.
- Expand brackets first.
- Collect like terms.
- Then undo adding or subtracting, and finally multiplying or dividing.
Example: 2(x + 3) = 14 Expand: 2x + 6 = 14. Subtract 6: 2x = 8. Divide by 2: x = 4. Answer: x = 4
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
Solve for x: 7(x + 7) = 42
answer box
-1
Hint: Divide both sides by 7: x + 7 = 6. Subtract 7: x = −1.
Question 2
Solve for x: 5x − 4 = 4x + 1
answer box
5
Hint: Collect the x terms: 5x − 4x = 1 − (−4), so 1x = 5. Divide by 1: x = 5.
Question 3
Solve for x: 8(x + 2) = 5(x − 5) + 53
answer box
4
Hint: Expand: 8x + 16 = 5x − 25 + 53. Collect: 3x = 12. Divide by 3: x = 4.
Question 4
Solve for x: x/4 + 9 = 10
answer box
4
Hint: Subtract 9: x/4 = 1. Multiply both sides by 4: x = 4.
Question 5
Solve for x: x/4 + x/3 = 35
answer box
60
Hint: Use a common denominator of 12: 3x/12 + 4x/12 = 35, so 7x = 420. Then x = 60.
Question 6
Jay's gym charges $40 to join plus $7 per visit. Another gym charges $100 to join plus $2 per visit. After how many visits do the two gyms cost the same?
answer box
12
Hint: Set the costs equal: 40 + 7n = 100 + 2n. Then 5n = 60, so n = 12.