Simple Linear Equations Worksheet featuring 12 algebraic problems to solve for variables, designed for educational practice.

Sure! Let’s solve each of the 12 linear equations step by step. The goal is to isolate the variable on one side of the equation using inverse operations (addition/subtraction, multiplication/division).

---

① 3y + 8 = 14

Step 1: Subtract 8 from both sides
→ 3y = 14 - 8
→ 3y = 6

Step 2: Divide both sides by 3
→ y = 6 ÷ 3
→ y = 2

---

② 2c + 7 = 21

Step 1: Subtract 7 from both sides
→ 2c = 21 - 7
→ 2c = 14

Step 2: Divide both sides by 2
→ c = 14 ÷ 2
→ c = 7

---

③ v/8 = -2

Step 1: Multiply both sides by 8 to eliminate denominator
→ v = -2 × 8
→ v = -16

---

④ n/12 = -5 - 11

Step 1: Simplify right-hand side
→ n/12 = -16

Step 2: Multiply both sides by 12
→ n = -16 × 12
→ n = -192

---

⑤ -3k = k + 2

Step 1: Subtract k from both sides to collect like terms
→ -3k - k = 2
→ -4k = 2

Step 2: Divide both sides by -4
→ k = 2 ÷ (-4)
→ k = -1/2

---

⑥ 1 = 10 - n

Step 1: Subtract 10 from both sides
→ 1 - 10 = -n
→ -9 = -n

Step 2: Multiply both sides by -1
→ n = 9

*(Alternatively: Add n to both sides → n + 1 = 10 → n = 9)*

---

⑦ 12 + x = -32

Step 1: Subtract 12 from both sides
→ x = -32 - 12
→ x = -44

---

⑧ 10 - 2 = p/9

Step 1: Simplify left-hand side
→ 8 = p/9

Step 2: Multiply both sides by 9
→ p = 8 × 9
→ p = 72

---

⑨ 3(x - 4) = 6

Step 1: Divide both sides by 3
→ x - 4 = 6 ÷ 3
→ x - 4 = 2

Step 2: Add 4 to both sides
→ x = 2 + 4
→ x = 6

---

⑩ -9x - 9x = -9

Step 1: Combine like terms on left
→ -18x = -9

Step 2: Divide both sides by -18
→ x = -9 ÷ (-18)
→ x = 1/2
→ x = 0.5

---

⑪ x/2 - x/3 = 1

Step 1: Find a common denominator for fractions (LCM of 2 and 3 is 6)
→ (3x)/6 - (2x)/6 = 1
→ (3x - 2x)/6 = 1
→ x/6 = 1

Step 2: Multiply both sides by 6
→ x = 6

---

⑫ 5/2 - x = 3x

Step 1: Add x to both sides to move all x terms to one side
→ 5/2 = 3x + x
→ 5/2 = 4x

Step 2: Divide both sides by 4
→ x = (5/2) ÷ 4
→ x = 5/2 × 1/4
→ x = 5/8
→ x = 0.625

---

## ✔ Final Answers:

1. y = 2
2. c = 7
3. v = -16
4. n = -192
5. k = -1/2
6. n = 9
7. x = -44
8. p = 72
9. x = 6
10. x = 1/2
11. x = 6
12. x = 5/8

Let me know if you’d like to see any step explained in more detail!