Simple Linear Equations worksheet with 15 algebra problems to solve for variables.

Sure! Let’s solve each of the 15 simple linear equations step by step. The goal is to isolate the variable on one side of the equation.

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1. `3b + 9 = -18`

Subtract 9 from both sides:
→ `3b = -18 - 9`
→ `3b = -27`

Divide both sides by 3:
→ `b = -27 / 3`
→ `b = -9`

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2. `3v + 1 = 22`

Subtract 1 from both sides:
→ `3v = 22 - 1`
→ `3v = 21`

Divide by 3:
→ `v = 21 / 3`
→ `v = 7`

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3. `3y - 2 = 10`

Add 2 to both sides:
→ `3y = 10 + 2`
→ `3y = 12`

Divide by 3:
→ `y = 12 / 3`
→ `y = 4`

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4. `2z + 1 = 15`

Subtract 1:
→ `2z = 15 - 1`
→ `2z = 14`

Divide by 2:
→ `z = 14 / 2`
→ `z = 7`

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5. `-2b - (-7) = 11`

Simplify: subtracting a negative is adding a positive:
→ `-2b + 7 = 11`

Subtract 7:
→ `-2b = 11 - 7`
→ `-2b = 4`

Divide by -2:
→ `b = 4 / (-2)`
→ `b = -2`

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6. `3c - 9 = -27`

Add 9 to both sides:
→ `3c = -27 + 9`
→ `3c = -18`

Divide by 3:
→ `c = -18 / 3`
→ `c = -6`

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7. `-3c - 4 = 2`

Add 4 to both sides:
→ `-3c = 2 + 4`
→ `-3c = 6`

Divide by -3:
→ `c = 6 / (-3)`
→ `c = -2`

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8. `-3c + 8 = -10`

Subtract 8:
→ `-3c = -10 - 8`
→ `-3c = -18`

Divide by -3:
→ `c = -18 / (-3)`
→ `c = 6`

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9. `2c - 8 = -18`

Add 8:
→ `2c = -18 + 8`
→ `2c = -10`

Divide by 2:
→ `c = -10 / 2`
→ `c = -5`

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10. `3a - 5 = -23`

Add 5:
→ `3a = -23 + 5`
→ `3a = -18`

Divide by 3:
→ `a = -18 / 3`
→ `a = -6`

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11. `-2a - 8 = -4`

Add 8:
→ `-2a = -4 + 8`
→ `-2a = 4`

Divide by -2:
→ `a = 4 / (-2)`
→ `a = -2`

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12. `3z - 2 = -26`

Add 2:
→ `3z = -26 + 2`
→ `3z = -24`

Divide by 3:
→ `z = -24 / 3`
→ `z = -8`

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13. `2a + 7 = 5`

Subtract 7:
→ `2a = 5 - 7`
→ `2a = -2`

Divide by 2:
→ `a = -2 / 2`
→ `a = -1`

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14. `3a - (-1) = -5`

Simplify: minus negative is plus:
→ `3a + 1 = -5`

Subtract 1:
→ `3a = -5 - 1`
→ `3a = -6`

Divide by 3:
→ `a = -6 / 3`
→ `a = -2`

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15. `-2a + (-1) = -13`

Simplify: adding negative is subtracting:
→ `-2a - 1 = -13`

Add 1:
→ `-2a = -13 + 1`
→ `-2a = -12`

Divide by -2:
→ `a = -12 / (-2)`
→ `a = 6`

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✔ Final Answers:

1. `b = -9`
2. `v = 7`
3. `y = 4`
4. `z = 7`
5. `b = -2`
6. `c = -6`
7. `c = -2`
8. `c = 6`
9. `c = -5`
10. `a = -6`
11. `a = -2`
12. `z = -8`
13. `a = -1`
14. `a = -2`
15. `a = 6`

Let me know if you’d like these explained in more detail or want to check your own work!