Grade 8 Patterns & Two-Step Equations worksheet
from Gradelings · Name: ______________________
How to explain it
- 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
Question 1
Solve for x: 8x + 3 = 75
answer box
9
Hint: Undo the addition first: 8x = 75 − 3 = 72. Then divide by 8: x = 9.
Question 2
Solve for x: x ÷ 3 + 3 = 7
answer box
12
Hint: Subtract 3: x ÷ 3 = 4. Multiply both sides by 3: x = 12.
Question 3
Solve for n: 30 = 6n + 18
answer box
2
Hint: Subtract 18 from both sides: 12 = 6n. Divide by 6: n = 2.
Question 4
Evaluate 6n + 7 when n = 6.
answer box
43
Hint: Replace n with 6: 6 × 6 + 7 = 36 + 7 = 43.
Question 5
Which expression means “3 more than 3 times a number n”?
- 6n
- 3n + 3
- 3(n + 3)
- 3n − 3
3n + 3
Hint: “3 times a number” is 3n. “3 more than” that means add 3: 3n + 3.
Question 6
I think of a number, multiply it by 4 and add 7. The result is 15. Which equation matches?
- n + 28 = 15
- 4n + 7 = 15
- 4(n + 7) = 15
- 4n − 7 = 15
- 4 + 7n = 15
4n + 7 = 15
Hint: "Multiply by 4" gives 4n, then "add 7" gives 4n + 7, and that equals 15.
Question 7
A school play charges a $3 booking fee plus $4 per ticket. How much do 11 tickets cost, in dollars?
answer box
47
Hint: Cost = 4 × 11 + 3 = 44 + 3 = 47. (You can only buy whole tickets, so this is a discrete relation.)
Question 8
A growing pattern of tiles follows the rule in the table. How many tiles are in figure 10?
Figure number (n) Number of tiles 1 7 2 12 3 17 4 22 answer box
52
Hint: The tiles go up by 5 each figure and figure 1 has 7. The rule is 5n + 2. For n = 10: 50 + 2 = 52.
Question 9
Is x = 8 a solution of 4x + 1 = 33?
- No
- Yes
Yes
Hint: Substitute x = 8: 4 × 8 + 1 = 33. That equals 33.
Question 10
Solve for x: 3x + 14 = 29
answer box
5
Hint: Undo the addition first: 3x = 29 − 14 = 15. Then divide by 3: x = 5.
Answer key
- 1. 9
- 2. 12
- 3. 2
- 4. 43
- 5. 3n + 3
- 6. 4n + 7 = 15
- 7. 47
- 8. 52
- 9. Yes
- 10. 5
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