Quiz Answers with Explanations

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📚 Part 1: Multiple Choice — Answers & Explanations

1. Solve: 3(x + 4) = 27

x = 3

x = 5 (Correct)

x = 7

x = 9

Explanation: Divide both sides by 3: x + 4 = 9, then subtract 4 to get x = 5. Check: 3(5+4)=27.

2. Solve: -2(3x - 5) = 14

x = -2/3 (Correct)

x = 2/3

x = -3

x = 3

Explanation: Divide by -2: 3x - 5 = -7. Add 5: 3x = -2. So x = -2/3. Substitute back to verify.

3. Which equation most directly requires using the distributive property to begin solving?

4(x + 2) = 16 (Correct)

7x + 3 = 24

x/3 + 5 = 9

(x + 1)^2 = 25

Explanation: Parentheses indicate we should distribute 4 first. The other equations can be solved without initial distribution.

4. Check all that apply: Which are correct applications of the distributive property?

2(x + 3) = 2x + 6 (Correct)

-3(x - 2) = -3x - 6

5(x + 0) = 5x + 0 (Correct)

(x + 2) + 3x = 4x + 2 (Correct)

Explanation: Distributing -3 through (x - 2) gives -3x + 6, not -3x - 6. The other three are algebraically correct.

✏️ Part 2: Short Answers — Worked Solutions

5. Solve and show steps: 5(x - 2) + 4 = 29

5(x - 2) + 4 = 29

Distribute: 5x - 10 + 4 = 29

Combine like terms: 5x - 6 = 29

Add 6: 5x = 35

Divide by 5: x = 7

Check: 5(7 - 2) + 4 = 25 + 4 = 29 ✓

6. Solve and show steps: 2(3x + 1) = 4x + 10

2(3x + 1) = 4x + 10

Distribute: 6x + 2 = 4x + 10

Subtract 4x: 2x + 2 = 10

Subtract 2: 2x = 8

Divide by 2: x = 4

Check: 2(3·4 + 1) = 2(13) = 26 and 4·4 + 10 = 26 ✓

7. Word problem: Jamie packs 3 boxes with (x + 2) toys each and gives away 5 toys. If 22 toys remain, find x.

Model: 3(x + 2) - 5 = 22

Distribute: 3x + 6 - 5 = 22

Simplify: 3x + 1 = 22

Subtract 1: 3x = 21

Divide by 3: x = 7

Check: Each box has 9 toys → 3·9 = 27, 27 - 5 = 22 ✓

8. Explain in one or two sentences: Why is the distributive property useful when solving equations?

Answer: The distributive property removes parentheses so you can combine like terms and isolate the variable. It makes equations easier to simplify and check, especially with negative signs or coefficients.

🧭 Teacher Notes, Success Criteria & Supports

I can... solve one-step and two-step equations that require the distributive property, including negatives and simple word problems.

Success criteria: Use the distributive property to remove parentheses, combine like terms, isolate the variable, and check the solution by substituting back into the original equation.

Differentiation strategies: Offer step-by-step templates and partially completed examples for students who need support; allow calculators for arithmetic; provide additional practice with positive/negative coefficients.

Extension: Challenge learners with distribution involving fractions or variables on both sides (example: (1/2)(4x + 6) = 10 or 2(x + 3) = x + 14).

Dyslexia-friendly options: Provide printed copies with larger sans-serif font and extra spacing, colored overlays on request, read problems aloud, and allow oral explanations or step-by-step scaffolds.