Linear Equation online exercise - Free Printable

Let's solve each of these linear equations step by step. These are all linear equations with one bracket, so we'll follow the standard method:

1. Expand the bracket (distribute the number outside the bracket).
2. Simplify both sides.
3. Isolate the variable (get the variable on one side and constants on the other).
4. Solve for the variable.

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1) $ 2(3a + 4) = 20 $

- Expand:
$ 2 \cdot 3a + 2 \cdot 4 = 6a + 8 $
- So:
$ 6a + 8 = 20 $
- Subtract 8 from both sides:
$ 6a = 12 $
- Divide by 6:
$ a = 2 $

✔ Answer: $ a = 2 $

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2) $ 3(3b - 5) = 12 $

- Expand:
$ 9b - 15 = 12 $
- Add 15 to both sides:
$ 9b = 27 $
- Divide by 9:
$ b = 3 $

✔ Answer: $ b = 3 $

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3) $ 5(2d + 1) = 55 $

- Expand:
$ 10d + 5 = 55 $
- Subtract 5:
$ 10d = 50 $
- Divide by 10:
$ d = 5 $

✔ Answer: $ d = 5 $

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4) $ 3(4h + 3) = 45 $

- Expand:
$ 12h + 9 = 45 $
- Subtract 9:
$ 12h = 36 $
- Divide by 12:
$ h = 3 $

✔ Answer: $ h = 3 $

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5) $ 9(5k + 8) = 72 $

- Expand:
$ 45k + 72 = 72 $
- Subtract 72:
$ 45k = 0 $
- Divide by 45:
$ k = 0 $

✔ Answer: $ k = 0 $

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6) $ 68 = 4(2c + 5) $

- Expand right side:
$ 68 = 8c + 20 $
- Subtract 20:
$ 48 = 8c $
- Divide by 8:
$ c = 6 $

✔ Answer: $ c = 6 $

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7) $ 54 = 2(5e - 8) $

- Expand:
$ 54 = 10e - 16 $
- Add 16:
$ 70 = 10e $
- Divide by 10:
$ e = 7 $

✔ Answer: $ e = 7 $

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8) $ 32 = 2(3f - 2) $

- Expand:
$ 32 = 6f - 4 $
- Add 4:
$ 36 = 6f $
- Divide by 6:
$ f = 6 $

✔ Answer: $ f = 6 $

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9) $ 6(2g + 3) + 2g = 74 $

- First expand:
$ 12g + 18 + 2g = 74 $
- Combine like terms:
$ 14g + 18 = 74 $
- Subtract 18:
$ 14g = 56 $
- Divide by 14:
$ g = 4 $

✔ Answer: $ g = 4 $

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10) $ 85 = 5(2x + 3) + 10 $

- Expand:
$ 85 = 10x + 15 + 10 $
- Simplify:
$ 85 = 10x + 25 $
- Subtract 25:
$ 60 = 10x $
- Divide by 10:
$ x = 6 $

✔ Answer: $ x = 6 $

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✔ Final Answers:

1) $ a = 2 $
2) $ b = 3 $
3) $ d = 5 $
4) $ h = 3 $
5) $ k = 0 $
6) $ c = 6 $
7) $ e = 7 $
8) $ f = 6 $
9) $ g = 4 $
10) $ x = 6 $

Let me know if you'd like these steps explained in a different way or formatted as a printable solution!