Grade 9 Multi-Step Equations worksheet
from Gradelings · Name: ______________________
How to explain it
- 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
Question 1
Solve for x: 6(x + 4) = 0
answer box
-4
Hint: Divide both sides by 6: x + 4 = 0. Subtract 4: x = −4.
Question 2
Solve for x: 3x − 6 = 1x + 16
answer box
11
Hint: Collect the x terms: 3x − 1x = 16 − (−6), so 2x = 22. Divide by 2: x = 11.
Question 3
Solve for x: 5(x + 2) = 3(x − 4) + 14
answer box
-4
Hint: Expand: 5x + 10 = 3x − 12 + 14. Collect: 2x = -8. Divide by 2: x = −4.
Question 4
Solve for x: x/5 + 5 = 9
answer box
20
Hint: Subtract 5: x/5 = 4. Multiply both sides by 5: x = 20.
Question 5
Solve for x: x/4 + x/3 = 28
answer box
48
Hint: Use a common denominator of 12: 3x/12 + 4x/12 = 28, so 7x = 336. Then x = 48.
Question 6
Noah's gym charges $20 to join plus $8 per visit. Another gym charges $35 to join plus $3 per visit. After how many visits do the two gyms cost the same?
answer box
3
Hint: Set the costs equal: 20 + 8n = 35 + 3n. Then 5n = 15, so n = 3.
Question 7
Is x = −5 the solution of 5x − 4 = −19?
- No
- Yes
No
Hint: Substitute: 5(−5) − 4 = −29, which does not equal −19.
Question 8
Twice a number, decreased by 3, is the same as 5 times the number plus 31. Which equation matches?
- 3 − 2n = 5n + 31
- 2(n − 3) = 5n + 31
- 2n − 3 = 5(n + 31)
- 2n + 3 = 5n + 31
- 2n − 3 = 5n + 31
2n − 3 = 5n + 31
Hint: “Twice a number, decreased by 3” is 2n − 3. “5 times the number plus 31” is 5n + 31. “Is the same as” means =.
Question 9
Solve for x: 7(x + 5) = −21
answer box
-8
Hint: Divide both sides by 7: x + 5 = −3. Subtract 5: x = −8.
Question 10
Solve for x: 3x + 1 = 1x − 11
answer box
-6
Hint: Collect the x terms: 3x − 1x = -11 − 1, so 2x = -12. Divide by 2: x = −6.
Answer key
- 1. -4
- 2. 11
- 3. -4
- 4. 20
- 5. 48
- 6. 3
- 7. No
- 8. 2n − 3 = 5n + 31
- 9. -8
- 10. -6
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