Let's solve each equation step by step. These are all
linear equations in one variable, and we'll solve for the unknown variable using basic algebraic operations (addition, subtraction, multiplication, division).
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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:
- Many answers repeat (like 4, 6), which is common in practice problems.
- The key idea is isolating the variable using inverse operations.
Let me know if you'd like this formatted as a printable answer sheet!
Parent Tip: Review the logic above to help your child master the concept of algebra math worksheets.
