Solving Basic Equations Worksheets - Free Printable

Let's solve each equation in the worksheet step by step. The goal is to solve for $ x $ in each linear equation.

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1. $-2x - 73 = -89$

Add 73 to both sides:
$$
-2x = -89 + 73 = -16
$$
Divide by -2:
$$
x = \frac{-16}{-2} = 8
$$
✔ $ x = 8 $

---

2. $-16x = -64$

Divide both sides by -16:
$$
x = \frac{-64}{-16} = 4
$$
✔ $ x = 4 $

---

3. $7x + 56 = -56$

Subtract 56 from both sides:
$$
7x = -56 - 56 = -112
$$
Divide by 7:
$$
x = \frac{-112}{7} = -16
$$
✔ $ x = -16 $

---

4. $5x - 63 = 17$

Add 63 to both sides:
$$
5x = 17 + 63 = 80
$$
Divide by 5:
$$
x = \frac{80}{5} = 16
$$
✔ $ x = 16 $

---

5. $8x + 11 = 75$

Subtract 11:
$$
8x = 75 - 11 = 64
$$
Divide by 8:
$$
x = \frac{64}{8} = 8
$$
✔ $ x = 8 $

---

6. $8x + 77 = -43$

Subtract 77:
$$
8x = -43 - 77 = -120
$$
Divide by 8:
$$
x = \frac{-120}{8} = -15
$$
✔ $ x = -15 $

---

7. $-11x - 27 = -49$

Add 27:
$$
-11x = -49 + 27 = -22
$$
Divide by -11:
$$
x = \frac{-22}{-11} = 2
$$
✔ $ x = 2 $

---

8. $18x + 75 = 21$

Subtract 75:
$$
18x = 21 - 75 = -54
$$
Divide by 18:
$$
x = \frac{-54}{18} = -3
$$
✔ $ x = -3 $

---

9. $-6x - 66 = 66$

Add 66:
$$
-6x = 66 + 66 = 132
$$
Divide by -6:
$$
x = \frac{132}{-6} = -22
$$
✔ $ x = -22 $

---

10. $-17x = 68$

Divide by -17:
$$
x = \frac{68}{-17} = -4
$$
✔ $ x = -4 $

---

11. $-5x + 67 = -48$

Subtract 67:
$$
-5x = -48 - 67 = -115
$$
Divide by -5:
$$
x = \frac{-115}{-5} = 23
$$
✔ $ x = 23 $

---

12. $12x = 36$

Divide by 12:
$$
x = \frac{36}{12} = 3
$$
✔ $ x = 3 $

---

13. $17x + 40 = 57$

Subtract 40:
$$
17x = 57 - 40 = 17
$$
Divide by 17:
$$
x = \frac{17}{17} = 1
$$
✔ $ x = 1 $

---

14. $12x + 33 = 93$

Subtract 33:
$$
12x = 93 - 33 = 60
$$
Divide by 12:
$$
x = \frac{60}{12} = 5
$$
✔ $ x = 5 $

---

15. $-3x - 95 = -8$

Add 95:
$$
-3x = -8 + 95 = 87
$$
Divide by -3:
$$
x = \frac{87}{-3} = -29
$$
✔ $ x = -29 $

---

16. $-6x - 4 = -10$

Add 4:
$$
-6x = -10 + 4 = -6
$$
Divide by -6:
$$
x = \frac{-6}{-6} = 1
$$
✔ $ x = 1 $

---

17. $2x - 3 = 9$

Add 3:
$$
2x = 9 + 3 = 12
$$
Divide by 2:
$$
x = \frac{12}{2} = 6
$$
✔ $ x = 6 $

---

18. $-19x - 15 = 4$

Add 15:
$$
-19x = 4 + 15 = 19
$$
Divide by -19:
$$
x = \frac{19}{-19} = -1
$$
✔ $ x = -1 $

---

19. $-19x - 87 = 8$

Add 87:
$$
-19x = 8 + 87 = 95
$$
Divide by -19:
$$
x = \frac{95}{-19} = -5
$$
✔ $ x = -5 $

---

20. $19x + 84 = -11$

Subtract 84:
$$
19x = -11 - 84 = -95
$$
Divide by 19:
$$
x = \frac{-95}{19} = -5
$$
✔ $ x = -5 $

---

21. $10x + 42 = -8$

Subtract 42:
$$
10x = -8 - 42 = -50
$$
Divide by 10:
$$
x = \frac{-50}{10} = -5
$$
✔ $ x = -5 $

---

22. $18x = 36$

Divide by 18:
$$
x = \frac{36}{18} = 2
$$
✔ $ x = 2 $

---

23. $-20x + 10 = -10$

Subtract 10:
$$
-20x = -10 - 10 = -20
$$
Divide by -20:
$$
x = \frac{-20}{-20} = 1
$$
✔ $ x = 1 $

---

24. $20x - 1 = 59$

Add 1:
$$
20x = 59 + 1 = 60
$$
Divide by 20:
$$
x = \frac{60}{20} = 3
$$
✔ $ x = 3 $

---

25. $14x + 43 = -83$

Subtract 43:
$$
14x = -83 - 43 = -126
$$
Divide by 14:
$$
x = \frac{-126}{14} = -9
$$
✔ $ x = -9 $

---

26. $5x - 25 = -5$

Add 25:
$$
5x = -5 + 25 = 20
$$
Divide by 5:
$$
x = \frac{20}{5} = 4
$$
✔ $ x = 4 $

---

27. $14x - 26 = -12$

Add 26:
$$
14x = -12 + 26 = 14
$$
Divide by 14:
$$
x = \frac{14}{14} = 1
$$
✔ $ x = 1 $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ x = 8 $ |
| 2 | $ x = 4 $ |
| 3 | $ x = -16 $ |
| 4 | $ x = 16 $ |
| 5 | $ x = 8 $ |
| 6 | $ x = -15 $ |
| 7 | $ x = 2 $ |
| 8 | $ x = -3 $ |
| 9 | $ x = -22 $ |
| 10 | $ x = -4 $ |
| 11 | $ x = 23 $ |
| 12 | $ x = 3 $ |
| 13 | $ x = 1 $ |
| 14 | $ x = 5 $ |
| 15 | $ x = -29 $ |
| 16 | $ x = 1 $ |
| 17 | $ x = 6 $ |
| 18 | $ x = -1 $ |
| 19 | $ x = -5 $ |
| 20 | $ x = -5 $ |
| 21 | $ x = -5 $ |
| 22 | $ x = 2 $ |
| 23 | $ x = 1 $ |
| 24 | $ x = 3 $ |
| 25 | $ x = -9 $ |
| 26 | $ x = 4 $ |
| 27 | $ x = 1 $ |

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🔍 Summary of Methods:

All equations are linear in one variable. To solve:
1. Isolate the variable term (move constants to the other side).
2. Divide by the coefficient of $ x $.
3. Always check signs carefully!

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