7th Grade Math Worksheet: Solving Equations

Let's solve each equation step by step. These are all one-step equations involving subtraction, so we'll solve them by adding the number being subtracted to both sides of the equation.

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1. $ x - 3 = 6 $

To isolate $ x $, add 3 to both sides:

$$
x - 3 + 3 = 6 + 3 \\
x = 9
$$

✔ Answer: $ x = 9 $

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2. $ x - 12 = 14 $

Add 12 to both sides:

$$
x - 12 + 12 = 14 + 12 \\
x = 26
$$

✔ Answer: $ x = 26 $

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3. $ n - 8 = 12 $

Add 8 to both sides:

$$
n - 8 + 8 = 12 + 8 \\
n = 20
$$

✔ Answer: $ n = 20 $

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4. $ a - 9 = 15 $

Add 9 to both sides:

$$
a - 9 + 9 = 15 + 9 \\
a = 24
$$

✔ Answer: $ a = 24 $

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5. $ n - 9 = 13 $

Add 9 to both sides:

$$
n - 9 + 9 = 13 + 9 \\
n = 22
$$

✔ Answer: $ n = 22 $

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6. $ b - 8 = 9 $

Add 8 to both sides:

$$
b - 8 + 8 = 9 + 8 \\
b = 17
$$

✔ Answer: $ b = 17 $

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7. $ x - 5 = 16 $

Add 5 to both sides:

$$
x - 5 + 5 = 16 + 5 \\
x = 21
$$

✔ Answer: $ x = 21 $

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8. $ n - 6 = 17 $

Add 6 to both sides:

$$
n - 6 + 6 = 17 + 6 \\
n = 23
$$

✔ Answer: $ n = 23 $

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✔ Final Answers:

1. $ x = 9 $
2. $ x = 26 $
3. $ n = 20 $
4. $ a = 24 $
5. $ n = 22 $
6. $ b = 17 $
7. $ x = 21 $
8. $ n = 23 $

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🔍 Explanation:

All these equations follow the form:
$$
\text{variable} - \text{number} = \text{result}
$$
To solve, you add the number to both sides to isolate the variable. This is based on the addition property of equality: if you do the same thing to both sides of an equation, it stays balanced.

This is a foundational skill in algebra — solving for unknowns by reversing operations. In this case, since subtraction is involved, we use addition to undo it.