Math worksheet for solving linear equations, divided into three sections with varying levels of difficulty.

Let's solve each equation step-by-step to find the value of $ x $. The goal is to isolate $ x $ on one side of the equation.

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Section A

1) $ 7x + 9 = 23 $
Subtract 9 from both sides:
$ 7x = 14 $
Divide by 7:
$ x = 2 $

2) $ 5x + 7 = 42 $
Subtract 7:
$ 5x = 35 $
Divide by 5:
$ x = 7 $

3) $ 4x + 3 = 51 $
Subtract 3:
$ 4x = 48 $
Divide by 4:
$ x = 12 $

4) $ 9x + 5 = 41 $
Subtract 5:
$ 9x = 36 $
Divide by 9:
$ x = 4 $

5) $ 4x + 2 = 34 $
Subtract 2:
$ 4x = 32 $
Divide by 4:
$ x = 8 $

6) $ 11x + 3 = 36 $
Subtract 3:
$ 11x = 33 $
Divide by 11:
$ x = 3 $

7) $ 10x + 2 = 72 $
Subtract 2:
$ 10x = 70 $
Divide by 10:
$ x = 7 $

8) $ 7x + 3 = 52 $
Subtract 3:
$ 7x = 49 $
Divide by 7:
$ x = 7 $

9) $ 6x + 5 = 17 $
Subtract 5:
$ 6x = 12 $
Divide by 6:
$ x = 2 $

10) $ 4x + 7 = 9 $
Subtract 7:
$ 4x = 2 $
Divide by 4:
$ x = \frac{1}{2} $

11) $ 8x + 11 = 15 $
Subtract 11:
$ 8x = 4 $
Divide by 8:
$ x = \frac{1}{2} $

12) $ 4x + 17 = 18 $
Subtract 17:
$ 4x = 1 $
Divide by 4:
$ x = \frac{1}{4} $

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Section B

1) $ 1 + 6x = 19 $
Subtract 1:
$ 6x = 18 $
Divide by 6:
$ x = 3 $

2) $ 9 + 7x = 30 $
Subtract 9:
$ 7x = 21 $
Divide by 7:
$ x = 3 $

3) $ 3 + 2x = 17 $
Subtract 3:
$ 2x = 14 $
Divide by 2:
$ x = 7 $

4) $ 11 + 5x = 71 $
Subtract 11:
$ 5x = 60 $
Divide by 5:
$ x = 12 $

5) $ 5 + 3x = 32 $
Subtract 5:
$ 3x = 27 $
Divide by 3:
$ x = 9 $

6) $ 4 + 5x = 44 $
Subtract 4:
$ 5x = 40 $
Divide by 5:
$ x = 8 $

7) $ 23 = x + 8 $
Subtract 8:
$ x = 15 $

8) $ 28 = 3x + 1 $
Subtract 1:
$ 27 = 3x $
Divide by 3:
$ x = 9 $

9) $ 53 = 8x + 5 $
Subtract 5:
$ 48 = 8x $
Divide by 8:
$ x = 6 $

10) $ 13 = 11 + 4x $
Subtract 11:
$ 2 = 4x $
Divide by 4:
$ x = \frac{1}{2} $

11) $ 7 = 8x + 3 $
Subtract 3:
$ 4 = 8x $
Divide by 8:
$ x = \frac{1}{2} $

12) $ 12 = 7 + 15x $
Subtract 7:
$ 5 = 15x $
Divide by 15:
$ x = \frac{1}{3} $

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Section C

1) $ 4x - 1 = 31 $
Add 1:
$ 4x = 32 $
Divide by 4:
$ x = 8 $

2) $ 3x - 4 = 29 $
Add 4:
$ 3x = 33 $
Divide by 3:
$ x = 11 $

3) $ 6x - 5 = 31 $
Add 5:
$ 6x = 36 $
Divide by 6:
$ x = 6 $

4) $ 8x - 2 = 46 $
Add 2:
$ 8x = 48 $
Divide by 8:
$ x = 6 $

5) $ 2x - 7 = 21 $
Add 7:
$ 2x = 28 $
Divide by 2:
$ x = 14 $

6) $ 7x - 3 = 18 $
Add 3:
$ 7x = 21 $
Divide by 7:
$ x = 3 $

7) $ 9x - 4 = 32 $
Add 4:
$ 9x = 36 $
Divide by 9:
$ x = 4 $

8) $ 5x - 1 = 64 $
Add 1:
$ 5x = 65 $
Divide by 5:
$ x = 13 $

9) $ 12x - 9 = 39 $
Add 9:
$ 12x = 48 $
Divide by 12:
$ x = 4 $

10) $ 2x - 1 = 2 $
Add 1:
$ 2x = 3 $
Divide by 2:
$ x = \frac{3}{2} $

11) $ 4x - 8 = 10 $
Add 8:
$ 4x = 18 $
Divide by 4:
$ x = \frac{9}{2} $

12) $ 15x - 2 = 3 $
Add 2:
$ 15x = 5 $
Divide by 15:
$ x = \frac{1}{3} $

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✔ Final Answers:

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

#### Section B
1) $ x = 3 $
2) $ x = 3 $
3) $ x = 7 $
4) $ x = 12 $
5) $ x = 9 $
6) $ x = 8 $
7) $ x = 15 $
8) $ x = 9 $
9) $ x = 6 $
10) $ x = \frac{1}{2} $
11) $ x = \frac{1}{2} $
12) $ x = \frac{1}{3} $

#### Section C
1) $ x = 8 $
2) $ x = 11 $
3) $ x = 6 $
4) $ x = 6 $
5) $ x = 14 $
6) $ x = 3 $
7) $ x = 4 $
8) $ x = 13 $
9) $ x = 4 $
10) $ x = \frac{3}{2} $
11) $ x = \frac{9}{2} $
12) $ x = \frac{1}{3} $

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🔍 Summary of Steps:

To solve linear equations like $ ax + b = c $, follow these steps:
1. Isolate the variable term by moving constants to the other side using addition/subtraction.
2. Divide both sides by the coefficient of $ x $ to solve for $ x $.

This method works for all linear equations in one variable.

Let me know if you'd like this formatted as a printable answer sheet!