Integers Worksheets for Grade 6 - Math Monks - Free Printable

Let's solve each equation step by step and find the value of each variable.

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1. $ a - 20 = 40 $

Add 20 to both sides:
$$
a = 40 + 20 = 60
$$
✔ $ a = 60 $

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2. $ 3e + 3 = 33 $

Subtract 3 from both sides:
$$
3e = 30
$$
Divide by 3:
$$
e = 10
$$
✔ $ e = 10 $

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3. $ 5k^2 - 90 = 410 $

Add 90 to both sides:
$$
5k^2 = 500
$$
Divide by 5:
$$
k^2 = 100
$$
Take square root:
$$
k = \pm 10
$$
✔ $ k = 10 $ or $ k = -10 $

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4. $ 5x^2 + 10 = 30 $

Subtract 10:
$$
5x^2 = 20
$$
Divide by 5:
$$
x^2 = 4
$$
Take square root:
$$
x = \pm 2
$$
✔ $ x = 2 $ or $ x = -2 $

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5. $ 3n^2 + 13 = 40 $

Subtract 13:
$$
3n^2 = 27
$$
Divide by 3:
$$
n^2 = 9
$$
Take square root:
$$
n = \pm 3
$$
✔ $ n = 3 $ or $ n = -3 $

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6. $ b - 20 = 30 $

Add 20:
$$
b = 50
$$
✔ $ b = 50 $

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7. $ n - 15 = -5 $

Add 15:
$$
n = 10
$$
✔ $ n = 10 $

> Note: This is a different $ n $ than in #5 — variables are independent.

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8. $ 3q^1 + 5 = 35 $

$ q^1 = q $, so:
$$
3q + 5 = 35
$$
Subtract 5:
$$
3q = 30
$$
Divide by 3:
$$
q = 10
$$
✔ $ q = 10 $

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9. $ -4a = 36 $

Divide by -4:
$$
a = -9
$$
✔ $ a = -9 $

> Note: Different from #1 — this is a separate equation.

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10. $ 3d + 10d = 130 $

Combine like terms:
$$
13d = 130
$$
Divide by 13:
$$
d = 10
$$
✔ $ d = 10 $

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11. $ 2x^2 - 4 = 4 $

Add 4:
$$
2x^2 = 8
$$
Divide by 2:
$$
x^2 = 4
$$
Take square root:
$$
x = \pm 2
$$
✔ $ x = 2 $ or $ x = -2 $

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12. $ t - 4 = 36 $

Add 4:
$$
t = 40
$$
✔ $ t = 40 $

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13. $ 2r - 5 = 7 $

Add 5:
$$
2r = 12
$$
Divide by 2:
$$
r = 6
$$
✔ $ r = 6 $

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14. $ 2y^2(4 - 2) = 16 $

Simplify inside parentheses:
$$
2y^2(2) = 16
\Rightarrow 4y^2 = 16
$$
Divide by 4:
$$
y^2 = 4
$$
Take square root:
$$
y = \pm 2
$$
✔ $ y = 2 $ or $ y = -2 $

---

15. $ -s + 26 = 6 $

Subtract 26:
$$
-s = -20
$$
Multiply by -1:
$$
s = 20
$$
✔ $ s = 20 $ (already given in red)

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16. $ 2n^1 + 20 = 26 $

$ n^1 = n $, so:
$$
2n + 20 = 26
$$
Subtract 20:
$$
2n = 6
$$
Divide by 2:
$$
n = 3
$$
✔ $ n = 3 $

> Note: Different from previous $ n $ values — again, independent.

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17. $ -3b + 40 = -5 $

Subtract 40:
$$
-3b = -45
$$
Divide by -3:
$$
b = 15
$$
✔ $ b = 15 $

> Note: Different from #6

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18. $ 4c = -20 $

Divide by 4:
$$
c = -5
$$
✔ $ c = -5 $

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19. $ 2q^2(2 + 1) = 216 $

Simplify:
$$
2q^2(3) = 216
\Rightarrow 6q^2 = 216
$$
Divide by 6:
$$
q^2 = 36
$$
Take square root:
$$
q = \pm 6
$$
✔ $ q = 6 $ or $ q = -6 $

> Note: Different from #8

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20. $ y - 15 = 5 $

Add 15:
$$
y = 20
$$
✔ $ y = 20 $

> Note: Different from #14

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21. $ 20 - 3f = 5 $

Subtract 20:
$$
-3f = -15
$$
Divide by -3:
$$
f = 5
$$
✔ $ f = 5 $

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✔ Final Answers:

| Equation | Solution |
|--------|---------|
| $ a - 20 = 40 $ | $ a = 60 $ |
| $ 3e + 3 = 33 $ | $ e = 10 $ |
| $ 5k^2 - 90 = 410 $ | $ k = \pm 10 $ |
| $ 5x^2 + 10 = 30 $ | $ x = \pm 2 $ |
| $ 3n^2 + 13 = 40 $ | $ n = \pm 3 $ |
| $ b - 20 = 30 $ | $ b = 50 $ |
| $ n - 15 = -5 $ | $ n = 10 $ |
| $ 3q + 5 = 35 $ | $ q = 10 $ |
| $ -4a = 36 $ | $ a = -9 $ |
| $ 3d + 10d = 130 $ | $ d = 10 $ |
| $ 2x^2 - 4 = 4 $ | $ x = \pm 2 $ |
| $ t - 4 = 36 $ | $ t = 40 $ |
| $ 2r - 5 = 7 $ | $ r = 6 $ |
| $ 2y^2(4 - 2) = 16 $ | $ y = \pm 2 $ |
| $ -s + 26 = 6 $ | $ s = 20 $ |
| $ 2n + 20 = 26 $ | $ n = 3 $ |
| $ -3b + 40 = -5 $ | $ b = 15 $ |
| $ 4c = -20 $ | $ c = -5 $ |
| $ 2q^2(2 + 1) = 216 $ | $ q = \pm 6 $ |
| $ y - 15 = 5 $ | $ y = 20 $ |
| $ 20 - 3f = 5 $ | $ f = 5 $ |

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💡 Note: Some variables appear multiple times (like $ a $, $ n $, $ q $, etc.), but each equation is independent. So their solutions are not related across equations.

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