Students can practice solving linear equations using the distributive property with this 12-problem algebra worksheet.

Sure! Let’s solve each equation step by step using the Distributive Property, which states:

> a(b + c) = ab + ac
> (or for subtraction: a(b - c) = ab - ac)

We’ll distribute the number outside the parentheses to each term inside, then solve for x.

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[1]  7(3x / 1) = -1

Note: 3x / 1 is just 3x.

→ 7 * 3x = -1
→ 21x = -1
→ x = -1/21

✔ Answer: x = -1/21

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[2]  -9(-3 - 8x) = -3

Distribute -9:

→ (-9)(-3) + (-9)(-8x) = -3
→ 27 + 72x = -3

Subtract 27 from both sides:

→ 72x = -3 - 27 = -30
→ x = -30 / 72 = -5/12 (simplify by dividing numerator and denominator by 6)

✔ Answer: x = -5/12

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[3]  1(7x - 1) = 6

Distribute 1 (which doesn’t change anything):

→ 7x - 1 = 6

Add 1 to both sides:

→ 7x = 7
→ x = 1

✔ Answer: x = 1

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[4]  -7(-7x + 9) = 5

Distribute -7:

→ (-7)(-7x) + (-7)(9) = 5
→ 49x - 63 = 5

Add 63 to both sides:

→ 49x = 68
→ x = 68/49

(Already simplified — 68 and 49 have no common factors)

✔ Answer: x = 68/49

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[5]  9(6x + 3) = 5

Distribute 9:

→ 54x + 27 = 5

Subtract 27:

→ 54x = 5 - 27 = -22
→ x = -22/54 = -11/27 (divide numerator and denominator by 2)

✔ Answer: x = -11/27

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[6]  -4(2x - 5) = 9

Distribute -4:

→ (-4)(2x) + (-4)(-5) = 9
→ -8x + 20 = 9

Subtract 20:

→ -8x = 9 - 20 = -11
→ x = (-11)/(-8) = 11/8

✔ Answer: x = 11/8

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[7]  -1(1x - 5) = 9

Distribute -1:

→ -1x + 5 = 9
→ -x + 5 = 9

Subtract 5:

→ -x = 4
→ x = -4

✔ Answer: x = -4

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[8]  6(-7x + 8) = 3

Distribute 6:

→ -42x + 48 = 3

Subtract 48:

→ -42x = 3 - 48 = -45
→ x = (-45)/(-42) = 15/14 (divide numerator and denominator by 3)

✔ Answer: x = 15/14

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[9]  7(-1 - 8x) = 8

Distribute 7:

→ 7*(-1) + 7*(-8x) = 8
→ -7 - 56x = 8

Add 7 to both sides:

→ -56x = 15
→ x = -15/56

✔ Answer: x = -15/56

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[10]  6(-5x - 5) = -3

Distribute 6:

→ -30x - 30 = -3

Add 30:

→ -30x = 27
→ x = 27 / (-30) = -9/10 (divide numerator and denominator by 3)

✔ Answer: x = -9/10

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[11]  -9(6x - 8) = -6

Distribute -9:

→ -54x + 72 = -6

Subtract 72:

→ -54x = -6 - 72 = -78
→ x = (-78)/(-54) = 13/9 (divide numerator and denominator by 6)

✔ Answer: x = 13/9

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[12]  10(-9 / 10x) = 8

This one is tricky. It says: 10 times (-9 divided by 10x)

So:
→ 10 * (-9 / (10x)) = 8

Simplify: The 10 in numerator and denominator cancel:

→ -9 / x = 8

Now solve for x:

→ -9 = 8x
→ x = -9/8

✔ Answer: x = -9/8

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## ✔ Final Answers:

[1] x = -1/21
[2] x = -5/12
[3] x = 1
[4] x = 68/49
[5] x = -11/27
[6] x = 11/8
[7] x = -4
[8] x = 15/14
[9] x = -15/56
[10] x = -9/10
[11] x = 13/9
[12] x = -9/8

Let me know if you’d like to see any step explained in more detail!