Solving Linear Equations (Without Negatives) Worksheet | Fun and ... - Free Printable

Let's solve each equation step-by-step, following the standard method for solving linear equations: isolate the variable $ x $ on one side of the equation using inverse operations.

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✔ Section A

1) $ 3x + 11 = 23 $
Subtract 11 from both sides:
$ 3x = 12 $
Divide by 3:
$ x = 4 $

2) $ 4x + 8 = 32 $
Subtract 8:
$ 4x = 24 $
Divide by 4:
$ x = 6 $

3) $ 7x - 9 = 12 $
Add 9:
$ 7x = 21 $
Divide by 7:
$ x = 3 $

4) $ 4x - 11 = 37 $
Add 11:
$ 4x = 48 $
Divide by 4:
$ x = 12 $

5) $ 6x + 7 = 55 $
Subtract 7:
$ 6x = 48 $
Divide by 6:
$ x = 8 $

6) $ 9x - 3 = 42 $
Add 3:
$ 9x = 45 $
Divide by 9:
$ x = 5 $

7) $ 4x + 10 = 12 $
Subtract 10:
$ 4x = 2 $
Divide by 4:
$ x = \frac{1}{2} $

8) $ 8x - 1 = 1 $
Add 1:
$ 8x = 2 $
Divide by 8:
$ x = \frac{1}{4} $

9) $ 48x - 7 = 9 $
Add 7:
$ 48x = 16 $
Divide by 48:
$ x = \frac{16}{48} = \frac{1}{3} $

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✔ Section B

1) $ 2(x + 7) = 30 $
Distribute:
$ 2x + 14 = 30 $
Subtract 14:
$ 2x = 16 $
Divide by 2:
$ x = 8 $

2) $ 3(x + 5) = 27 $
Distribute:
$ 3x + 15 = 27 $
Subtract 15:
$ 3x = 12 $
Divide by 3:
$ x = 4 $

3) $ 5(x - 9) = 55 $
Distribute:
$ 5x - 45 = 55 $
Add 45:
$ 5x = 100 $
Divide by 5:
$ x = 20 $

4) $ 4(3x + 6) = 48 $
Distribute:
$ 12x + 24 = 48 $
Subtract 24:
$ 12x = 24 $
Divide by 12:
$ x = 2 $

5) $ 7(4x - 12) = 56 $
Distribute:
$ 28x - 84 = 56 $
Add 84:
$ 28x = 140 $
Divide by 28:
$ x = 5 $

6) $ 2(8x - 60) = 24 $
Distribute:
$ 16x - 120 = 24 $
Add 120:
$ 16x = 144 $
Divide by 16:
$ x = 9 $

7) $ 2(4x + 22) = 48 $
Distribute:
$ 8x + 44 = 48 $
Subtract 44:
$ 8x = 4 $
Divide by 8:
$ x = \frac{1}{2} $

8) $ 9(12x + 4) = 72 $
Distribute:
$ 108x + 36 = 72 $
Subtract 36:
$ 108x = 36 $
Divide by 108:
$ x = \frac{36}{108} = \frac{1}{3} $

9) $ 12(30x - 3) = 36 $
Distribute:
$ 360x - 36 = 36 $
Add 36:
$ 360x = 72 $
Divide by 360:
$ x = \frac{72}{360} = \frac{1}{5} $

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✔ Section C

1) $ x + 8 = 9x $
Subtract $ x $:
$ 8 = 8x $
Divide by 8:
$ x = 1 $

2) $ 30 + x = 7x $
Subtract $ x $:
$ 30 = 6x $
Divide by 6:
$ x = 5 $

3) $ 2x + 16 = 6x $
Subtract $ 2x $:
$ 16 = 4x $
Divide by 4:
$ x = 4 $

4) $ 96 - 5x = 7x $
Add $ 5x $:
$ 96 = 12x $
Divide by 12:
$ x = 8 $

5) $ 70 - 6x = 4x $
Add $ 6x $:
$ 70 = 10x $
Divide by 10:
$ x = 7 $

6) $ 132 - 9x = 3x $
Add $ 9x $:
$ 132 = 12x $
Divide by 12:
$ x = 11 $

7) $ 6(x + 5) = 8x $
Distribute:
$ 6x + 30 = 8x $
Subtract $ 6x $:
$ 30 = 2x $
Divide by 2:
$ x = 15 $

8) $ 6(12 - 3x) = 6x $
Distribute:
$ 72 - 18x = 6x $
Add $ 18x $:
$ 72 = 24x $
Divide by 24:
$ x = 3 $

9) $ 4(1 - 2x) = 12x $
Distribute:
$ 4 - 8x = 12x $
Add $ 8x $:
$ 4 = 20x $
Divide by 20:
$ x = \frac{1}{5} $

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✔ Section D

1) $ 9x - 2 = 2x + 12 $
Subtract $ 2x $:
$ 7x - 2 = 12 $
Add 2:
$ 7x = 14 $
Divide by 7:
$ x = 2 $

2) $ 12x + 4 = 31 + 3x $
Subtract $ 3x $:
$ 9x + 4 = 31 $
Subtract 4:
$ 9x = 27 $
Divide by 9:
$ x = 3 $

3) $ 46 + 3x = 8x - 14 $
Subtract $ 3x $:
$ 46 = 5x - 14 $
Add 14:
$ 60 = 5x $
Divide by 5:
$ x = 12 $

4) $ 87 + 2x = 6 + 11x $
Subtract $ 2x $:
$ 87 = 6 + 9x $
Subtract 6:
$ 81 = 9x $
Divide by 9:
$ x = 9 $

5) $ 14x - 23 = 2x + 1 $
Subtract $ 2x $:
$ 12x - 23 = 1 $
Add 23:
$ 12x = 24 $
Divide by 12:
$ x = 2 $

6) $ 5x - 6 = 48 - 13x $
Add $ 13x $:
$ 18x - 6 = 48 $
Add 6:
$ 18x = 54 $
Divide by 18:
$ x = 3 $

7) $ 69 - 15x = 24 - 6x $
Add $ 15x $:
$ 69 = 24 + 9x $
Subtract 24:
$ 45 = 9x $
Divide by 9:
$ x = 5 $

8) $ 8x - 21 = 86 - 2x $
Add $ 2x $:
$ 10x - 21 = 86 $
Add 21:
$ 10x = 107 $
Divide by 10:
$ x = 10.7 $

9) $ 16x + 13 = 22x - 77 $
Subtract $ 16x $:
$ 13 = 6x - 77 $
Add 77:
$ 90 = 6x $
Divide by 6:
$ x = 15 $

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✔ Final Answers:

#### Section A
1) $ x = 4 $
2) $ x = 6 $
3) $ x = 3 $
4) $ x = 12 $
5) $ x = 8 $
6) $ x = 5 $
7) $ x = \frac{1}{2} $
8) $ x = \frac{1}{4} $
9) $ x = \frac{1}{3} $

#### Section B
1) $ x = 8 $
2) $ x = 4 $
3) $ x = 20 $
4) $ x = 2 $
5) $ x = 5 $
6) $ x = 9 $
7) $ x = \frac{1}{2} $
8) $ x = \frac{1}{3} $
9) $ x = \frac{1}{5} $

#### Section C
1) $ x = 1 $
2) $ x = 5 $
3) $ x = 4 $
4) $ x = 8 $
5) $ x = 7 $
6) $ x = 11 $
7) $ x = 15 $
8) $ x = 3 $
9) $ x = \frac{1}{5} $

#### Section D
1) $ x = 2 $
2) $ x = 3 $
3) $ x = 12 $
4) $ x = 9 $
5) $ x = 2 $
6) $ x = 3 $
7) $ x = 5 $
8) $ x = 10.7 $
9) $ x = 15 $

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✔ All solutions are non-negative, as required.

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