Solving Equations With Distributive Property Worksheet - Free Printable

Let's solve each equation step by step using algebraic techniques, including the distributive property where applicable. However, note that none of these equations involve parentheses where the distributive property (like $ a(b + c) = ab + ac $) would directly apply. Instead, these are linear equations in one variable that require combining like terms and isolating the variable.

We'll solve each equation using standard algebraic methods:

---

1. $ 21k + 19 = 67 + 20k $

- Subtract $ 20k $ from both sides:
$$
21k - 20k + 19 = 67
\Rightarrow k + 19 = 67
$$
- Subtract 19 from both sides:
$$
k = 67 - 19 = 48
$$

✔ Answer: $ k = 48 $

---

2. $ 20a + 15 = 47 + 19a $

- Subtract $ 19a $ from both sides:
$$
20a - 19a + 15 = 47
\Rightarrow a + 15 = 47
$$
- Subtract 15:
$$
a = 47 - 15 = 32
$$

✔ Answer: $ a = 32 $

---

3. $ 5z - 11 = 39 + 4z $

- Subtract $ 4z $ from both sides:
$$
5z - 4z - 11 = 39
\Rightarrow z - 11 = 39
$$
- Add 11:
$$
z = 39 + 11 = 50
$$

✔ Answer: $ z = 50 $

---

4. $ -3a + 17 = 61 - 4a $

- Add $ 4a $ to both sides:
$$
-3a + 4a + 17 = 61
\Rightarrow a + 17 = 61
$$
- Subtract 17:
$$
a = 61 - 17 = 44
$$

✔ Answer: $ a = 44 $

---

5. $ 11h + 10 = 68 + 10h $

- Subtract $ 10h $:
$$
11h - 10h + 10 = 68
\Rightarrow h + 10 = 68
$$
- Subtract 10:
$$
h = 68 - 10 = 58
$$

✔ Answer: $ h = 58 $

---

6. $ 4v + 35 = 106 + 3v $

- Subtract $ 3v $:
$$
4v - 3v + 35 = 106
\Rightarrow v + 35 = 106
$$
- Subtract 35:
$$
v = 106 - 35 = 71
$$

✔ Answer: $ v = 71 $

---

7. $ 21p - 19 = -8 + 20p $

- Subtract $ 20p $:
$$
21p - 20p - 19 = -8
\Rightarrow p - 19 = -8
$$
- Add 19:
$$
p = -8 + 19 = 11
$$

✔ Answer: $ p = 11 $

---

8. $ 12r + 10 = 77 + 11r $

- Subtract $ 11r $:
$$
12r - 11r + 10 = 77
\Rightarrow r + 10 = 77
$$
- Subtract 10:
$$
r = 77 - 10 = 67
$$

✔ Answer: $ r = 67 $

---

9. $ 22a - 4 = 48 + 21a $

- Subtract $ 21a $:
$$
22a - 21a - 4 = 48
\Rightarrow a - 4 = 48
$$
- Add 4:
$$
a = 48 + 4 = 52
$$

✔ Answer: $ a = 52 $

---

10. $ 19l - 15 = 20 + 18l $

- Subtract $ 18l $:
$$
19l - 18l - 15 = 20
\Rightarrow l - 15 = 20
$$
- Add 15:
$$
l = 20 + 15 = 35
$$

✔ Answer: $ l = 35 $

---

✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ k = 48 $ |
| 2 | $ a = 32 $ |
| 3 | $ z = 50 $ |
| 4 | $ a = 44 $ |
| 5 | $ h = 58 $ |
| 6 | $ v = 71 $ |
| 7 | $ p = 11 $ |
| 8 | $ r = 67 $ |
| 9 | $ a = 52 $ |
| 10 | $ l = 35 $ |

---

🔍 Explanation:

Although the worksheet says "use the distributive property", these problems do not require it because there are no expressions with parentheses that need distribution (e.g., $ a(b + c) $). Instead, they are one-step or two-step linear equations solved by:

1. Moving all variable terms to one side.
2. Moving constants to the other.
3. Solving for the variable.

The distributive property is more relevant when expanding expressions like $ 3(x + 4) = 3x + 12 $. But here, we're just simplifying and solving equations through combining like terms and inverse operations.

Let me know if you'd like a version with distributive property applied explicitly!