Practice Algebra Equations | Worksheet - Free Printable

Let's solve each of the algebra equations step by step.

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Part 1: Solve for x

#### 1.) $ 18 + 2x = 24 $

Subtract 18 from both sides:
$$
2x = 24 - 18 = 6
$$
Divide by 2:
$$
x = \frac{6}{2} = 3
$$
✔ Answer: $ x = 3 $

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#### 2.) $ 4x - 3 = 21 $

Add 3 to both sides:
$$
4x = 24
$$
Divide by 4:
$$
x = \frac{24}{4} = 6
$$
✔ Answer: $ x = 6 $

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#### 3.) $ 2x + 10 = 20 $

Subtract 10 from both sides:
$$
2x = 10
$$
Divide by 2:
$$
x = 5
$$
✔ Answer: $ x = 5 $

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#### 4.) $ 8x - 6 = 18 $

Add 6 to both sides:
$$
8x = 24
$$
Divide by 8:
$$
x = 3
$$
✔ Answer: $ x = 3 $

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#### 5.) $ 12 + 3x = 27 $

Subtract 12 from both sides:
$$
3x = 15
$$
Divide by 3:
$$
x = 5
$$
✔ Answer: $ x = 5 $

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#### 6.) $ 5x - 7 = 18 $

Add 7 to both sides:
$$
5x = 25
$$
Divide by 5:
$$
x = 5
$$
✔ Answer: $ x = 5 $

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#### 7.) $ 3(x + 3) - x = 17 $

Distribute:
$$
3x + 9 - x = 17
$$
Combine like terms:
$$
2x + 9 = 17
$$
Subtract 9:
$$
2x = 8
$$
Divide by 2:
$$
x = 4
$$
✔ Answer: $ x = 4 $

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#### 8.) $ 22 - 2x + 4(x - 2) = 34 $

Distribute:
$$
22 - 2x + 4x - 8 = 34
$$
Simplify:
$$
(22 - 8) + (-2x + 4x) = 34 \\
14 + 2x = 34
$$
Subtract 14:
$$
2x = 20
$$
Divide by 2:
$$
x = 10
$$
✔ Answer: $ x = 10 $

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#### 9.) $ 7x - 4(x + 4) + 20 = 25 $

Distribute:
$$
7x - 4x - 16 + 20 = 25
$$
Simplify:
$$
3x + 4 = 25
$$
Subtract 4:
$$
3x = 21
$$
Divide by 3:
$$
x = 7
$$
✔ Answer: $ x = 7 $

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#### 10.) $ 11 + 5x + 2(x - 5) = 8 $

Distribute:
$$
11 + 5x + 2x - 10 = 8
$$
Simplify:
$$
(11 - 10) + (5x + 2x) = 8 \\
1 + 7x = 8
$$
Subtract 1:
$$
7x = 7
$$
Divide by 7:
$$
x = 1
$$
✔ Answer: $ x = 1 $

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Part 2: Solve for x, when y equals the number given

#### 1.) $ y = 6, x = ? $
Equation: $ 7x - 2 + 4y = 36 $

Substitute $ y = 6 $:
$$
7x - 2 + 4(6) = 36 \\
7x - 2 + 24 = 36 \\
7x + 22 = 36
$$
Subtract 22:
$$
7x = 14
$$
Divide by 7:
$$
x = 2
$$
✔ Answer: $ x = 2 $

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#### 2.) $ y = 3, x = ? $
Equation: $ 2y + 8 + 5x = 29 $

Substitute $ y = 3 $:
$$
2(3) + 8 + 5x = 29 \\
6 + 8 + 5x = 29 \\
14 + 5x = 29
$$
Subtract 14:
$$
5x = 15
$$
Divide by 5:
$$
x = 3
$$
✔ Answer: $ x = 3 $

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#### 3.) $ y = 4, x = ? $
Equation: $ 6(x - 1) + y = 22 $

Substitute $ y = 4 $:
$$
6(x - 1) + 4 = 22 \\
6x - 6 + 4 = 22 \\
6x - 2 = 22
$$
Add 2:
$$
6x = 24
$$
Divide by 6:
$$
x = 4
$$
✔ Answer: $ x = 4 $

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#### 4.) $ y = 5, x = ? $
Equation: $ y + 4(5 - 3x) = 13 $

Substitute $ y = 5 $:
$$
5 + 4(5 - 3x) = 13 \\
5 + 20 - 12x = 13 \\
25 - 12x = 13
$$
Subtract 25:
$$
-12x = -12
$$
Divide by -12:
$$
x = 1
$$
✔ Answer: $ x = 1 $

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✔ Final Answers Summary:

#### Part 1:
1. $ x = 3 $
2. $ x = 6 $
3. $ x = 5 $
4. $ x = 3 $
5. $ x = 5 $
6. $ x = 5 $
7. $ x = 4 $
8. $ x = 10 $
9. $ x = 7 $
10. $ x = 1 $

#### Part 2:
1. $ x = 2 $
2. $ x = 3 $
3. $ x = 4 $
4. $ x = 1 $

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