Distributive Property Practice Worksheet with 12 problems for solving equations using the distributive property.

It looks like you've uploaded a worksheet titled "Distributive Property" with 12 problems. The instructions say:
> *"Solve for x. None of the equations contain decimals. You may use your calculator."*

However, I can't see the image directly since it's not visible in this interface. But based on the text you've provided, here are the 12 equations:

1. \( 3(1 - 2x) = 51 \)
2. \( 4(-1 + 6) = 16 \) ← Wait — this one doesn't have an \( x \). Let’s double-check.

Wait — looking at the list:

1. \( 3(1 - 2x) = 51 \)
2. \( 4(-1 + 6) = 16 \) ← This is not an equation to solve for \( x \), because there's no variable. It's just a computation.

Let me check all the equations again from your text:

1. \( 3(1 - 2x) = 51 \)
2. \( 4(-1 + 6) = 16 \) → This appears to be a computational expression, not an equation in \( x \).
3. \( 2(-8 - 3x) = 90 \)
4. \( 7(6x - 8) = 476 \)
5. \( 3(2 - 4x) = -90 \)
6. \( 2(-3 + 4x) = 18 \)
7. \( 5(7 + 2x) = 155 \)
8. \( -7(2 - 6x) = 196 \)
9. \( 7(3x + 7) = 280 \)
10. \( 5(9 - 6x) = 225 \)
11. \( -7(6 - 3x) = -273 \)
12. \( -6(8 + 4x) = -216 \)

But Problem 2 is suspicious:
\( 4(-1 + 6) = 16 \) → That's just \( 4(5) = 20 \), which is not equal to 16, so it's either a typo or not meant to be solved.

Possibility: Maybe it was meant to be:
- \( 4(-1 + 6x) = 16 \)? Or
- \( 4(x - 1) = 16 \)?

But as written, it's not solvable for \( x \) because there's no variable.

Let’s assume that Problem 2 is a typo and perhaps should be something like:
\( 4(-1 + 6x) = 16 \) — but we’ll proceed with the rest, and flag Problem 2.

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Let’s solve each equation using the distributive property and algebra.

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#### 1. \( 3(1 - 2x) = 51 \)

Distribute:
\( 3 \cdot 1 - 3 \cdot 2x = 51 \)
\( 3 - 6x = 51 \)

Subtract 3:
\( -6x = 48 \)

Divide by -6:
\( x = -8 \)

✔ Answer: \( x = -8 \)

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#### 2. \( 4(-1 + 6) = 16 \)

This is not an equation with a variable.
Compute:
\( 4(5) = 20 \neq 16 \)

So this is false as written. Likely a typo.

Assuming it was meant to be:
\( 4(-1 + 6x) = 16 \)

Then:
Distribute: \( -4 + 24x = 16 \)
Add 4: \( 24x = 20 \)
\( x = \frac{20}{24} = \frac{5}{6} \)

But since it's written as \( 4(-1 + 6) = 16 \), and it's false, maybe it's a mistake.

Alternatively, maybe it's supposed to be:
\( 4(x - 1) = 16 \) → then \( x - 1 = 4 \) → \( x = 5 \)

But without clarification, we'll skip this for now and move on.

⚠️ Note: Problem 2 is likely incorrect or missing a variable.

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#### 3. \( 2(-8 - 3x) = 90 \)

Distribute:
\( -16 - 6x = 90 \)

Add 16:
\( -6x = 106 \)

Divide by -6:
\( x = -\frac{106}{6} = -\frac{53}{3} \approx -17.67 \)

But the directions say "none of the equations contain decimals", so this suggests a possible error.

Wait — let's double-check:
\( 2(-8 - 3x) = 90 \) → \( -16 - 6x = 90 \) → \( -6x = 106 \) → \( x = -106/6 = -53/3 \)

That’s a fraction, not a decimal, so it's acceptable (fractions are allowed).

✔ Answer: \( x = -\frac{53}{3} \)

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#### 4. \( 7(6x - 8) = 476 \)

Distribute:
\( 42x - 56 = 476 \)

Add 56:
\( 42x = 532 \)

Divide by 42:
\( x = \frac{532}{42} \)

Simplify: divide numerator and denominator by 2:
\( \frac{266}{21} \approx 12.666... \)

Again, a fraction — but okay.

Wait: Is this correct? Let's check:

\( 7(6x - 8) = 476 \)
Try \( x = 12 \): \( 6(12) = 72 \), \( 72 - 8 = 64 \), \( 7×64 = 448 \) → too low
Try \( x = 13 \): \( 6×13 = 78 \), \( 78 - 8 = 70 \), \( 7×70 = 490 \) → too high
So between 12 and 13.

But let’s compute exactly:

\( x = \frac{532}{42} = \frac{266}{21} = 12 \frac{14}{21} = 12 \frac{2}{3} \)

So \( x = \frac{266}{21} \)

✔ Answer: \( x = \frac{266}{21} \)

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#### 5. \( 3(2 - 4x) = -90 \)

Distribute:
\( 6 - 12x = -90 \)

Subtract 6:
\( -12x = -96 \)

Divide by -12:
\( x = 8 \)

✔ Answer: \( x = 8 \)

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#### 6. \( 2(-3 + 4x) = 18 \)

Distribute:
\( -6 + 8x = 18 \)

Add 6:
\( 8x = 24 \)

Divide by 8:
\( x = 3 \)

✔ Answer: \( x = 3 \)

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#### 7. \( 5(7 + 2x) = 155 \)

Distribute:
\( 35 + 10x = 155 \)

Subtract 35:
\( 10x = 120 \)

Divide by 10:
\( x = 12 \)

✔ Answer: \( x = 12 \)

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#### 8. \( -7(2 - 6x) = 196 \)

Distribute:
\( -14 + 42x = 196 \)

Add 14:
\( 42x = 210 \)

Divide by 42:
\( x = 5 \)

✔ Answer: \( x = 5 \)

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#### 9. \( 7(3x + 7) = 280 \)

Distribute:
\( 21x + 49 = 280 \)

Subtract 49:
\( 21x = 231 \)

Divide by 21:
\( x = 11 \)

✔ Answer: \( x = 11 \)

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#### 10. \( 5(9 - 6x) = 225 \)

Distribute:
\( 45 - 30x = 225 \)

Subtract 45:
\( -30x = 180 \)

Divide by -30:
\( x = -6 \)

✔ Answer: \( x = -6 \)

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#### 11. \( -7(6 - 3x) = -273 \)

Distribute:
\( -42 + 21x = -273 \)

Add 42:
\( 21x = -231 \)

Divide by 21:
\( x = -11 \)

✔ Answer: \( x = -11 \)

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#### 12. \( -6(8 + 4x) = -216 \)

Distribute:
\( -48 - 24x = -216 \)

Add 48:
\( -24x = -168 \)

Divide by -24:
\( x = 7 \)

✔ Answer: \( x = 7 \)

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Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | \( x = -8 \) |
| 2 | ✘ Invalid (no variable; likely typo) |
| 3 | \( x = -\frac{53}{3} \) |
| 4 | \( x = \frac{266}{21} \) |
| 5 | \( x = 8 \) |
| 6 | \( x = 3 \) |
| 7 | \( x = 12 \) |
| 8 | \( x = 5 \) |
| 9 | \( x = 11 \) |
| 10 | \( x = -6 \) |
| 11 | \( x = -11 \) |
| 12 | \( x = 7 \) |

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Notes:

- Problem 2 seems incorrect as written. If it was meant to be \( 4(x - 1) = 16 \), then \( x = 5 \).
- All other problems follow the distributive property:
\( a(b + c) = ab + ac \)
- Then solve for \( x \) using inverse operations.

If you can clarify Problem 2, I can fix it.

Let me know if you'd like these answers formatted differently or checked step-by-step!