Let's solve each of these pre-algebra equations step by step. These are all
linear equations in one variable, and we'll solve them by isolating the variable on one side.
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Problem 1:
4a + 15 = 31
Subtract 15 from both sides:
4a = 31 - 15 = 16
Divide both sides by 4:
a = 16 ÷ 4 =
4
✔ a = 4
---
Problem 2:
5x + 8 = 18
Subtract 8 from both sides:
5x = 18 - 8 = 10
Divide by 5:
x = 10 ÷ 5 =
2
✔ x = 2
---
Problem 3:
3a + 12 = 24
Subtract 12:
3a = 24 - 12 = 12
Divide by 3:
a = 12 ÷ 3 =
4
✔ a = 4
---
Problem 4:
5c + 2 = 22
Subtract 2:
5c = 20
Divide by 5:
c = 20 ÷ 5 =
4
✔ c = 4
---
Problem 5:
4x - 9 = 7
Add 9 to both sides:
4x = 7 + 9 = 16
Divide by 4:
x = 16 ÷ 4 =
4
✔ x = 4
---
Problem 6:
x + 1 = 4
Subtract 1:
x = 4 - 1 =
3
✔ x = 3
---
Problem 7:
6x - 3 = 3
Add 3:
6x = 6
Divide by 6:
x = 6 ÷ 6 =
1
✔ x = 1
---
Problem 8:
2a + 2 = 8
Subtract 2:
2a = 6
Divide by 2:
a = 6 ÷ 2 =
3
✔ a = 3
---
Problem 9:
6a + 8 = 32
Subtract 8:
6a = 24
Divide by 6:
a = 24 ÷ 6 =
4
✔ a = 4
---
Problem 10:
4x - 6 = 2
Add 6:
4x = 8
Divide by 4:
x = 8 ÷ 4 =
2
✔ x = 2
---
Problem 11:
3x - 2 = 10
Add 2:
3x = 12
Divide by 3:
x = 12 ÷ 3 =
4
✔ x = 4
---
Problem 12:
a + 1 = 5
Subtract 1:
a = 5 - 1 =
4
✔ a = 4
---
Problem 13:
c + 1 = 3
Subtract 1:
c = 3 - 1 =
2
✔ c = 2
---
Problem 14:
3b - 4 = 14
Add 4:
3b = 18
Divide by 3:
b = 18 ÷ 3 =
6
✔ b = 6
---
Problem 15:
6a - 13 = 11
Add 13:
6a = 24
Divide by 6:
a = 24 ÷ 6 =
4
✔ a = 4
---
Problem 16:
6b - 36 = 0
Add 36:
6b = 36
Divide by 6:
b = 36 ÷ 6 =
6
✔ b = 6
---
Problem 17:
4b - 9 = 15
Add 9:
4b = 24
Divide by 4:
b = 24 ÷ 4 =
6
✔ b = 6
---
Problem 18:
6b - 12 = 18
Add 12:
6b = 30
Divide by 6:
b = 30 ÷ 6 =
5
✔ b = 5
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✔ Final Answers:
| Problem | Answer |
|--------|--------|
| ① | a = 4 |
| ② | x = 2 |
| ③ | a = 4 |
| ④ | c = 4 |
| ⑤ | x = 4 |
| ⑥ | x = 3 |
| ⑦ | x = 1 |
| ⑧ | a = 3 |
| ⑨ | a = 4 |
| ⑩ | x = 2 |
| ⑪ | x = 4 |
| ⑫ | a = 4 |
| ⑬ | c = 2 |
| ⑭ | b = 6 |
| ⑮ | a = 4 |
| ⑯ | b = 6 |
| ⑰ | b = 6 |
| ⑱ | b = 5 |
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🔍 Summary:
Most of the answers are integers, and many variables (especially 'a') turn out to be
4, which might be intentional for practice. The key skill here is
isolating the variable using inverse operations (addition/subtraction, multiplication/division).
Let me know if you'd like this as a printable answer sheet!
Parent Tip: Review the logic above to help your child master the concept of free pre algebra worksheet with answer key.
