Solving algebraic equations worksheets | Worsheets library - Free Printable

Let's solve each of the 20 basic algebra equations from the worksheet step by step. The goal is to solve for the variable $ x $ in each equation, and express the answer as "$ x = $" (e.g., $ x = 5 $).

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1) $ x + 12 = 14 $

Subtract 12 from both sides:
$ x = 14 - 12 $
$ x = 2 $

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2) $ 11 + x = 15 $

Subtract 11 from both sides:
$ x = 15 - 11 $
$ x = 4 $

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3) $ x - 5 = 6 $

Add 5 to both sides:
$ x = 6 + 5 $
$ x = 11 $

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4) $ 2 + x = 8 $

Subtract 2 from both sides:
$ x = 8 - 2 $
$ x = 6 $

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5) $ x - 3 = 2 $

Add 3 to both sides:
$ x = 2 + 3 $
$ x = 5 $

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6) $ x - 6 = 6 $

Add 6 to both sides:
$ x = 6 + 6 $
$ x = 12 $

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7) $ 7 + x = 14 $

Subtract 7 from both sides:
$ x = 14 - 7 $
$ x = 7 $

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8) $ 12 - x = 7 $

Subtract 12 from both sides:
$ -x = 7 - 12 $
$ -x = -5 $
Multiply both sides by -1:
$ x = 5 $

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9) $ 5 + x = 9 $

Subtract 5 from both sides:
$ x = 9 - 5 $
$ x = 4 $

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10) $ x - 10 = 2 $

Add 10 to both sides:
$ x = 2 + 10 $
$ x = 12 $

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11) $ x + 6 = 14 $

Subtract 6 from both sides:
$ x = 14 - 6 $
$ x = 8 $

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12) $ 7 + x = 10 $

Subtract 7 from both sides:
$ x = 10 - 7 $
$ x = 3 $

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13) $ 10 - x = 7 $

Subtract 10 from both sides:
$ -x = 7 - 10 $
$ -x = -3 $
Multiply both sides by -1:
$ x = 3 $

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14) $ 8 + x = 15 $

Subtract 8 from both sides:
$ x = 15 - 8 $
$ x = 7 $

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15) $ 8 - x = 1 $

Subtract 8 from both sides:
$ -x = 1 - 8 $
$ -x = -7 $
Multiply both sides by -1:
$ x = 7 $

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16) $ x + 10 = 14 $

Subtract 10 from both sides:
$ x = 14 - 10 $
$ x = 4 $

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17) $ x - 3 = 8 $

Add 3 to both sides:
$ x = 8 + 3 $
$ x = 11 $

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18) $ x + 7 = 9 $

Subtract 7 from both sides:
$ x = 9 - 7 $
$ x = 2 $

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19) $ x + 7 = 19 $

Subtract 7 from both sides:
$ x = 19 - 7 $
$ x = 12 $

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20) $ x + 2 = 10 $

Subtract 2 from both sides:
$ x = 10 - 2 $
$ x = 8 $

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✔ Final Answers:

1) $ x = 2 $
2) $ x = 4 $
3) $ x = 11 $
4) $ x = 6 $
5) $ x = 5 $
6) $ x = 12 $
7) $ x = 7 $
8) $ x = 5 $
9) $ x = 4 $
10) $ x = 12 $
11) $ x = 8 $
12) $ x = 3 $
13) $ x = 3 $
14) $ x = 7 $
15) $ x = 7 $
16) $ x = 4 $
17) $ x = 11 $
18) $ x = 2 $
19) $ x = 12 $
20) $ x = 8 $

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🔍 Explanation:

These are all one-step linear equations, meaning you only need one operation (addition or subtraction) to isolate $ x $. The key idea is to perform the inverse operation on both sides of the equation to get $ x $ alone.

- If $ x $ is being added to a number, subtract that number from both sides.
- If $ x $ is being subtracted from a number, add that number to both sides.
- If $ x $ has a number subtracted from it, add that number to both sides.

This reinforces foundational algebra skills for Grade 5 Pre-Algebra.

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