Linear Equation Worksheets (printable, online, answers, examples) - Free Printable

Let's solve each of the linear equations step by step.

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1. $ 5x + 2(2x - 4) = 55 $

Step 1: Distribute the 2 into the parentheses:
$$
5x + 2 \cdot 2x - 2 \cdot 4 = 55 \\
5x + 4x - 8 = 55
$$

Step 2: Combine like terms:
$$
9x - 8 = 55
$$

Step 3: Add 8 to both sides:
$$
9x = 63
$$

Step 4: Divide by 9:
$$
x = 7
$$

✔ Answer: $ x = 7 $

---

2. $ 7x + 4(x - 9) = 41 $

Step 1: Distribute the 4:
$$
7x + 4x - 36 = 41
$$

Step 2: Combine like terms:
$$
11x - 36 = 41
$$

Step 3: Add 36 to both sides:
$$
11x = 77
$$

Step 4: Divide by 11:
$$
x = 7
$$

✔ Answer: $ x = 7 $

---

3. $ 3x + 2(x - 6) = 33 $

Step 1: Distribute the 2:
$$
3x + 2x - 12 = 33
$$

Step 2: Combine like terms:
$$
5x - 12 = 33
$$

Step 3: Add 12 to both sides:
$$
5x = 45
$$

Step 4: Divide by 5:
$$
x = 9
$$

✔ Answer: $ x = 9 $

---

4. $ 4x + 3(3x + 7) = 86 $

Step 1: Distribute the 3:
$$
4x + 9x + 21 = 86
$$

Step 2: Combine like terms:
$$
13x + 21 = 86
$$

Step 3: Subtract 21 from both sides:
$$
13x = 65
$$

Step 4: Divide by 13:
$$
x = 5
$$

✔ Answer: $ x = 5 $

---

5. $ 2x + 5(4x - 7) = 75 $

Step 1: Distribute the 5:
$$
2x + 20x - 35 = 75
$$

Step 2: Combine like terms:
$$
22x - 35 = 75
$$

Step 3: Add 35 to both sides:
$$
22x = 110
$$

Step 4: Divide by 22:
$$
x = 5
$$

✔ Answer: $ x = 5 $

---

6. $ 97 = 7x + 2(x + 8) $

Step 1: Distribute the 2:
$$
97 = 7x + 2x + 16
$$

Step 2: Combine like terms:
$$
97 = 9x + 16
$$

Step 3: Subtract 16 from both sides:
$$
81 = 9x
$$

Step 4: Divide by 9:
$$
x = 9
$$

✔ Answer: $ x = 9 $

---

7. $ 6x + 5(2x - 7) = 45 $

Step 1: Distribute the 5:
$$
6x + 10x - 35 = 45
$$

Step 2: Combine like terms:
$$
16x - 35 = 45
$$

Step 3: Add 35 to both sides:
$$
16x = 80
$$

Step 4: Divide by 16:
$$
x = 5
$$

✔ Answer: $ x = 5 $

---

8. $ 63 = 6x + 3(3x - 4) $

Step 1: Distribute the 3:
$$
63 = 6x + 9x - 12
$$

Step 2: Combine like terms:
$$
63 = 15x - 12
$$

Step 3: Add 12 to both sides:
$$
75 = 15x
$$

Step 4: Divide by 15:
$$
x = 5
$$

✔ Answer: $ x = 5 $

---

9. $ 3x + 4(x + 6) = 59 $

Step 1: Distribute the 4:
$$
3x + 4x + 24 = 59
$$

Step 2: Combine like terms:
$$
7x + 24 = 59
$$

Step 3: Subtract 24 from both sides:
$$
7x = 35
$$

Step 4: Divide by 7:
$$
x = 5
$$

✔ Answer: $ x = 5 $

---

10. $ 82 = 2x + 2(3x + 5) $

Step 1: Distribute the 2:
$$
82 = 2x + 6x + 10
$$

Step 2: Combine like terms:
$$
82 = 8x + 10
$$

Step 3: Subtract 10 from both sides:
$$
72 = 8x
$$

Step 4: Divide by 8:
$$
x = 9
$$

✔ Answer: $ x = 9 $

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✔ Final Answers:

| Equation | Solution |
|--------|---------|
| $ 5x + 2(2x - 4) = 55 $ | $ x = 7 $ |
| $ 7x + 4(x - 9) = 41 $ | $ x = 7 $ |
| $ 3x + 2(x - 6) = 33 $ | $ x = 9 $ |
| $ 4x + 3(3x + 7) = 86 $ | $ x = 5 $ |
| $ 2x + 5(4x - 7) = 75 $ | $ x = 5 $ |
| $ 97 = 7x + 2(x + 8) $ | $ x = 9 $ |
| $ 6x + 5(2x - 7) = 45 $ | $ x = 5 $ |
| $ 63 = 6x + 3(3x - 4) $ | $ x = 5 $ |
| $ 3x + 4(x + 6) = 59 $ | $ x = 5 $ |
| $ 82 = 2x + 2(3x + 5) $ | $ x = 9 $ |

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💡 Summary:
Most of these equations simplify to $ x = 5 $ or $ x = 7 $ or $ x = 9 $. The key steps are:
- Distribute (use distributive property),
- Combine like terms,
- Isolate the variable using inverse operations.

Let me know if you'd like a visual explanation or practice problems!