Solving Equations with Distributive Property (Day 1) online ... - Free Printable

Sure! Let’s solve each equation step by step using the Distributive Property and inverse operations, as shown in the examples.

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🔢 Problem 1: `3(2x + 10) = 54`

Step 1: Distribute 3 to both terms inside the parentheses.
→ `6x + 30 = 54`

Step 2: Subtract 30 from both sides.
→ `6x = 24`

Step 3: Divide both sides by 6.
→ `x = 4`

✔ Answer: x = 4

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🔢 Problem 2: `6(4x + 1) = 78`

Step 1: Distribute 6.
→ `24x + 6 = 78`

Step 2: Subtract 6 from both sides.
→ `24x = 72`

Step 3: Divide by 24.
→ `x = 3`

✔ Answer: x = 3

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🔢 Problem 3: `2(x + 10) = 60`

Step 1: Distribute 2.
→ `2x + 20 = 60`

Step 2: Subtract 20.
→ `2x = 40`

Step 3: Divide by 2.
→ `x = 20`

✔ Answer: x = 20

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🔢 Problem 4: `4(3x + 2) = 68`

Step 1: Distribute 4.
→ `12x + 8 = 68`

Step 2: Subtract 8.
→ `12x = 60`

Step 3: Divide by 12.
→ `x = 5`

✔ Answer: x = 5

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🔢 Problem 5: `9(2 + 3x) = 45`

Step 1: Distribute 9.
→ `18 + 27x = 45`

Step 2: Subtract 18.
→ `27x = 27`

Step 3: Divide by 27.
→ `x = 1`

✔ Answer: x = 1

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🔢 Problem 6: `8(4 + x) = 64`

Step 1: Distribute 8.
→ `32 + 8x = 64`

Step 2: Subtract 32.
→ `8x = 32`

Step 3: Divide by 8.
→ `x = 4`

✔ Answer: x = 4

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🔢 Problem 7: `2(10 + 10x) = 60`

Step 1: Distribute 2.
→ `20 + 20x = 60`

Step 2: Subtract 20.
→ `20x = 40`

Step 3: Divide by 20.
→ `x = 2`

✔ Answer: x = 2

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🔢 Problem 8: `4(3 + 2x) = 76`

Step 1: Distribute 4.
→ `12 + 8x = 76`

Step 2: Subtract 12.
→ `8x = 64`

Step 3: Divide by 8.
→ `x = 8`

✔ Answer: x = 8

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🔢 Problem 9: `5(2x + 10) = 50`

Step 1: Distribute 5.
→ `10x + 50 = 50`

Step 2: Subtract 50.
→ `10x = 0`

Step 3: Divide by 10.
→ `x = 0`

✔ Answer: x = 0

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🔢 Problem 10: `2(12 + 3x) = 42`

Step 1: Distribute 2.
→ `24 + 6x = 42`

Step 2: Subtract 24.
→ `6x = 18`

Step 3: Divide by 6.
→ `x = 3`

✔ Answer: x = 3

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🔢 Problem 11: `15(x + 3) = 60`

Step 1: Distribute 15.
→ `15x + 45 = 60`

Step 2: Subtract 45.
→ `15x = 15`

Step 3: Divide by 15.
→ `x = 1`

✔ Answer: x = 1

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🔢 Problem 12: `2(20 + 2x) = 80`

Step 1: Distribute 2.
→ `40 + 4x = 80`

Step 2: Subtract 40.
→ `4x = 40`

Step 3: Divide by 4.
→ `x = 10`

✔ Answer: x = 10

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## ✔ Final Answers:

1) x = 4
2) x = 3
3) x = 20
4) x = 5
5) x = 1
6) x = 4
7) x = 2
8) x = 8
9) x = 0
10) x = 3
11) x = 1
12) x = 10

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Let me know if you’d like to see an alternative method (like dividing first, as in Example 2) for any of these!