Solving Equations With Distributive Property Worksheet - Free Printable

Let’s solve each equation step by step. We’ll move all the variable terms (like k, a, z, etc.) to one side and all the numbers to the other side. Then we’ll simplify and solve for the variable.

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1. 21k + 19 = 67 + 20k

Subtract 20k from both sides:
→ 21k - 20k + 19 = 67
→ k + 19 = 67

Subtract 19 from both sides:
→ k = 67 - 19
→ k = 48

✔ Check: 21(48) + 19 = 1008 + 19 = 1027; 67 + 20(48) = 67 + 960 = 1027 → Correct.

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2. 20a + 15 = 47 + 19a

Subtract 19a from both sides:
→ 20a - 19a + 15 = 47
→ a + 15 = 47

Subtract 15 from both sides:
→ a = 47 - 15
→ a = 32

✔ Check: 20(32)+15=640+15=655; 47+19(32)=47+608=655 → Correct.

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3. 5z - 11 = 39 + 4z

Subtract 4z from both sides:
→ 5z - 4z - 11 = 39
→ z - 11 = 39

Add 11 to both sides:
→ z = 39 + 11
→ z = 50

✔ Check: 5(50)-11=250-11=239; 39+4(50)=39+200=239 → Correct.

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

Add 4a to both sides:
→ -3a + 4a + 17 = 61
→ a + 17 = 61

Subtract 17 from both sides:
→ a = 61 - 17
→ a = 44

✔ Check: -3(44)+17=-132+17=-115; 61-4(44)=61-176=-115 → Correct.

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5. 11h + 10 = 68 + 10h

Subtract 10h from both sides:
→ 11h - 10h + 10 = 68
→ h + 10 = 68

Subtract 10 from both sides:
→ h = 68 - 10
→ h = 58

✔ Check: 11(58)+10=638+10=648; 68+10(58)=68+580=648 → Correct.

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6. 4v + 35 = 106 + 3v

Subtract 3v from both sides:
→ 4v - 3v + 35 = 106
→ v + 35 = 106

Subtract 35 from both sides:
→ v = 106 - 35
→ v = 71

✔ Check: 4(71)+35=284+35=319; 106+3(71)=106+213=319 → Correct.

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

Subtract 20p from both sides:
→ 21p - 20p - 19 = -8
→ p - 19 = -8

Add 19 to both sides:
→ p = -8 + 19
→ p = 11

✔ Check: 21(11)-19=231-19=212; -8+20(11)=-8+220=212 → Correct.

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8. 12r + 10 = 77 + 11r

Subtract 11r from both sides:
→ 12r - 11r + 10 = 77
→ r + 10 = 77

Subtract 10 from both sides:
→ r = 77 - 10
→ r = 67

✔ Check: 12(67)+10=804+10=814; 77+11(67)=77+737=814 → Correct.

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9. 22a - 4 = 48 + 21a

Subtract 21a from both sides:
→ 22a - 21a - 4 = 48
→ a - 4 = 48

Add 4 to both sides:
→ a = 48 + 4
→ a = 52

✔ Check: 22(52)-4=1144-4=1140; 48+21(52)=48+1092=1140 → Correct.

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10. 19l - 15 = 20 + 18l

Subtract 18l from both sides:
→ 19l - 18l - 15 = 20
→ l - 15 = 20

Add 15 to both sides:
→ l = 20 + 15
→ l = 35

✔ Check: 19(35)-15=665-15=650; 20+18(35)=20+630=650 → Correct.

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Final 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