Grade 8 · Math · Unit 9 of 18
Patterns & Two-Step Equations
Expressions, patterns and solving for x
What your child practises
Writing and evaluating expressions like 3n + 2, solving two-step equations, and finding the rule for a growing pattern or a cost made of whole items such as tickets.
Ontario Curriculum expectation: C1.3, C2.2, C2.3 · pattern rules, evaluating expressions and solving equations
How we explain it
Children can open this short lesson before they practise.
- Do the same thing to both sides to keep the equation balanced.
- Undo adding and subtracting first.
- Then undo multiplying and dividing.
Example: 3x − 5 = 16 Add 5 to both sides: 3x = 21. Divide both sides by 3: x = 7. Answer: x = 7
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: 6x + 1 = 49
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8
Hint: Undo the addition first: 6x = 49 − 1 = 48. Then divide by 6: x = 8.
Question 2
Solve for x: x ÷ 4 + 6 = 9
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12
Hint: Subtract 6: x ÷ 4 = 3. Multiply both sides by 4: x = 12.
Question 3
Solve for n: 72 = 6n + 18
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9
Hint: Subtract 18 from both sides: 54 = 6n. Divide by 6: n = 9.
Question 4
Evaluate 6n + 4 when n = 6.
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40
Hint: Replace n with 6: 6 × 6 + 4 = 36 + 4 = 40.
Question 5
Which expression means “4 more than 4 times a number n”?
- 4n − 4
- 4n + 4
- 4(n + 4)
- 8n
Show answer
4n + 4
Hint: “4 times a number” is 4n. “4 more than” that means add 4: 4n + 4.
Question 6
I think of a number, multiply it by 4 and add 11. The result is 43. Which equation matches?
- 4(n + 11) = 43
- 4n + 11 = 43
- 4n − 11 = 43
- 4 + 11n = 43
- n + 44 = 43
Show answer
4n + 11 = 43
Hint: "Multiply by 4" gives 4n, then "add 11" gives 4n + 11, and that equals 43.