Set of 20 numbered algebra problems requiring students to isolate x.

Let's solve each of these linear equations step by step. The goal is to isolate $ x $ on one side of the equation.

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1) $ 2x + 4 = 14 $

Subtract 4 from both sides:
$ 2x = 10 $
Divide by 2:
$ x = 5 $

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2) $ 4x + 7 = 19 $

Subtract 7:
$ 4x = 12 $
Divide by 4:
$ x = 3 $

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3) $ 6x + 5 = 23 $

Subtract 5:
$ 6x = 18 $
Divide by 6:
$ x = 3 $

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4) $ 2x + 11 = 27 $

Subtract 11:
$ 2x = 16 $
Divide by 2:
$ x = 8 $

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5) $ 5x + 9 = 29 $

Subtract 9:
$ 5x = 20 $
Divide by 5:
$ x = 4 $

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6) $ 7x + 13 = 34 $

Subtract 13:
$ 7x = 21 $
Divide by 7:
$ x = 3 $

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7) $ 4x + 3 = 35 $

Subtract 3:
$ 4x = 32 $
Divide by 4:
$ x = 8 $

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8) $ 6x + 18 = 24 $

Subtract 18:
$ 6x = 6 $
Divide by 6:
$ x = 1 $

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9) $ 9x + 5 = 104 $

Subtract 5:
$ 9x = 99 $
Divide by 9:
$ x = 11 $

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10) $ 6x + 11 = 65 $

Subtract 11:
$ 6x = 54 $
Divide by 6:
$ x = 9 $

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11) $ 3x - 7 = 20 $

Add 7:
$ 3x = 27 $
Divide by 3:
$ x = 9 $

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12) $ 10x - 10 = 30 $

Add 10:
$ 10x = 40 $
Divide by 10:
$ x = 4 $

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13) $ 6x - 2 = 28 $

Add 2:
$ 6x = 30 $
Divide by 6:
$ x = 5 $

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14) $ 3x - 5 = 13 $

Add 5:
$ 3x = 18 $
Divide by 3:
$ x = 6 $

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15) $ 5x - 8 = 27 $

Add 8:
$ 5x = 35 $
Divide by 5:
$ x = 7 $

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16) $ 4x - 7 = 1 $

Add 7:
$ 4x = 8 $
Divide by 4:
$ x = 2 $

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17) $ 8x - 6 = 18 $

Add 6:
$ 8x = 24 $
Divide by 8:
$ x = 3 $

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18) $ 7x - 11 = 17 $

Add 11:
$ 7x = 28 $
Divide by 7:
$ x = 4 $

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19) $ 9x - 21 = 60 $

Add 21:
$ 9x = 81 $
Divide by 9:
$ x = 9 $

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20) $ 2x - 9 = 15 $

Add 9:
$ 2x = 24 $
Divide by 2:
$ x = 12 $

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✔ Final Answers:

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

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🔍 Summary:

All equations are linear in the form $ ax + b = c $. The general method is:
1. Move constants to the right side (add or subtract).
2. Divide both sides by the coefficient of $ x $.

Let me know if you'd like a visual explanation or help with graphing!