Grade 7 Two-Step Equations worksheet
from Gradelings · Name: ______________________
How to explain it
- Keep the equation balanced: do the same to both sides.
- Undo the adding or subtracting first.
- Then undo the multiplying or dividing.
Example: 2x + 3 = 11 Subtract 3 from both sides: 2x = 8. Divide both sides by 2: x = 4. Answer: x = 4
Question 1
Is x = 8 a solution of 2x − 17 = 1?
2x − 17 = 1
- No
- Yes
No
Hint: Substitute x = 8: 2 × 8 − 17 = -1. That isn't 1, so x = 8 is not a solution.
Question 2
Solve for x.
8x + 30 = 70
answer box
5
Hint: Undo the + 30 first: subtract 30 from both sides to get 8x = 40. Then undo the × 8: divide both sides by 8 to get x = 5.
Question 3
Which equation matches this sentence? "Two times a number, plus 4, equals 32."
- 2n + 4 = 32
- 2n − 4 = 32
- 4n + 2 = 32
- 2(n + 4) = 32
2n + 4 = 32
Hint: "Two times a number" is 2n. "Plus 4" adds 4 after multiplying: 2n + 4. "Equals 32" finishes it: 2n + 4 = 32.
Question 4
Solve: 9n − 21 = 15
- 3
- 5
- 4
- 36
4
Hint: Undo the − 21 first: add 21 to both sides to get 9n = 36. Then divide both sides by 9: n = 4.
Question 5
To solve 9x + 7 = 124, how do you undo the + 7?
- Subtract 7 from the left side only
- Add 7 to both sides
- Subtract 7 from both sides
- Divide both sides by 7
Subtract 7 from both sides
Hint: Use the opposite operation, and keep the equation balanced by doing it to both sides. The opposite of adding 7 is subtracting 7.
Question 6
A rectangle has a perimeter of 88 cm and a width of 16 cm. What is its length?
answer boxcm
28 cm
Hint: Perimeter = 2L + 2w, so 2L + 32 = 88. Subtract 32: 2L = 56. Divide by 2: L = 28 cm.
Question 7
On a balance scale, 7 identical bags of marbles plus 9 loose marbles balance 58 loose marbles. How many marbles are in each bag?
⚖️7x + 9 = 58answer box
7
Hint: Take 9 marbles off both sides: 7 bags balance 49 marbles. Share them among 7 bags: 49 ÷ 7 = 7.
Question 8
Is x = 2 a solution of 3x + 6 = 12?
3x + 6 = 12
- No
- Yes
Yes
Hint: Substitute x = 2: 3 × 2 + 6 = 12. That equals 12, so x = 2 works.
Question 9
To solve 5x + 9 = 24, how do you undo the + 9?
- Add 9 to both sides
- Divide both sides by 9
- Subtract 9 from both sides
- Subtract 9 from the left side only
Subtract 9 from both sides
Hint: Use the opposite operation, and keep the equation balanced by doing it to both sides. The opposite of adding 9 is subtracting 9.
Question 10
Which equation matches this sentence? "Four times a number, minus 6, equals 10."
- 4n + 6 = 10
- 6n − 4 = 10
- 4n − 6 = 10
- 4(n − 6) = 10
4n − 6 = 10
Hint: "Four times a number" is 4n. "Minus 6" subtracts 6 after multiplying: 4n − 6. "Equals 10" finishes it: 4n − 6 = 10.
Answer key
- 1. No
- 2. 5
- 3. 2n + 4 = 32
- 4. 4
- 5. Subtract 7 from both sides
- 6. 28 cm
- 7. 7
- 8. Yes
- 9. Subtract 9 from both sides
- 10. 4n − 6 = 10
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