Solve linear equations in one variable with this printable worksheet from Math Monks, featuring ten problems with varying coefficients and operations.

Sure! Let’s solve each of the 10 linear equations step by step. The goal is to isolate the variable on one side of the equation.

---

① 12 - x = 7

Subtract 12 from both sides:
→ -x = 7 - 12
→ -x = -5

Multiply both sides by -1:
→ x = 5

✔ Answer: x = 5

---

② 9 + 6x = 3x + 13

Subtract 3x from both sides:
→ 9 + 3x = 13

Subtract 9 from both sides:
→ 3x = 4

Divide by 3:
→ x = 4/3

✔ Answer: x = 4/3

---

③ 10x + 3 + 10x = 13x - 3

Combine like terms on left:
→ 20x + 3 = 13x - 3

Subtract 13x from both sides:
→ 7x + 3 = -3

Subtract 3 from both sides:
→ 7x = -6

Divide by 7:
→ x = -6/7

✔ Answer: x = -6/7

---

④ 0.25(60) + 0.10x = 0.15(60 + x)

First, compute 0.25 × 60 = 15
Compute right side: 0.15(60 + x) = 9 + 0.15x

So:
→ 15 + 0.10x = 9 + 0.15x

Subtract 0.10x from both sides:
→ 15 = 9 + 0.05x

Subtract 9:
→ 6 = 0.05x

Divide by 0.05 (or multiply by 20):
→ x = 120

✔ Answer: x = 120

---

⑤ 3 = 4(x - 2) + 5 - 4x

Distribute the 4:
→ 3 = 4x - 8 + 5 - 4x

Simplify right side:
→ 3 = (4x - 4x) + (-8 + 5)
→ 3 = 0 - 3
→ 3 = -3 ✘

This is a contradiction — no solution.

✔ Answer: No solution

---

⑥ (5y)/9 - 3 = 6

Add 3 to both sides:
→ (5y)/9 = 9

Multiply both sides by 9:
→ 5y = 81

Divide by 5:
→ y = 81/5 = 16.2

✔ Answer: y = 81/5 or 16.2

---

⑦ n/10 = 9 - n/4

Eliminate fractions by multiplying entire equation by LCM of 10 and 4 → 20:

20 × (n/10) = 20 × (9 - n/4)
→ 2n = 180 - 5n

Add 5n to both sides:
→ 7n = 180

Divide by 7:
→ n = 180/7

✔ Answer: n = 180/7

---

⑧ 21.1w + 4.6 = 10.9w

Subtract 10.9w from both sides:
→ 10.2w + 4.6 = 0

Subtract 4.6:
→ 10.2w = -4.6

Divide by 10.2:
→ w = -4.6 / 10.2

Multiply numerator and denominator by 10 to eliminate decimals:
→ w = -46 / 102

Simplify by dividing numerator and denominator by 2:
→ w = -23/51

✔ Answer: w = -23/51

---

⑨ -5(3 - 4x) = -6 + 20x

Distribute -5:
→ -15 + 20x = -6 + 20x

Subtract 20x from both sides:
→ -15 = -6 ✘

Contradiction — no solution

✔ Answer: No solution

---

⑩ 9.2z - 4.3 = 50.8

Add 4.3 to both sides:
→ 9.2z = 55.1

Divide by 9.2:
→ z = 55.1 / 9.2

Multiply numerator and denominator by 10:
→ z = 551 / 92

Simplify? Let’s check GCD of 551 and 92.

92 = 2×2×23
551 ÷ 23 = 23.956… → not divisible.

Check 551 ÷ 19 = 29 → 19×29=551
92 ÷ 19? No. So no common factors.

→ z = 551/92 (or as decimal ≈ 5.989)

But let’s verify with decimal:

55.1 ÷ 9.2 = ?

9.2 × 6 = 55.2 → too big
9.2 × 5.99 = 9.2 × 6 - 9.2 × 0.01 = 55.2 - 0.092 = 55.108 → close to 55.1

Actually, 55.1 ÷ 9.2 = 551 ÷ 92 = 5.98913...

But since the problem likely expects exact form:

✔ Answer: z = 551/92

*(Alternatively, if decimal is acceptable: z ≈ 5.99)*

---

## ✔ Final Answers Summary:

1. x = 5
2. x = 4/3
3. x = -6/7
4. x = 120
5. No solution
6. y = 81/5
7. n = 180/7
8. w = -23/51
9. No solution
10. z = 551/92

Let me know if you want these in decimal form or need any step explained further!