Quiz Answer Explanations

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📚 Part 1: Multiple Choice — Answers & Explanations

1. Solve: 3x + 5 = 20

x = 5

x = 6

x = 3

x = -5

Answer: x = 5. Explanation: Subtract 5 from both sides to get 3x = 15, then divide by 3 to get x = 5. Check: 3(5)+5 = 20.

2. Solve: (1/2)x - 4 = 6

x = 20

x = 12

x = -20

x = 2

Answer: x = 20. Explanation: Add 4 to both sides: (1/2)x = 10. Multiply both sides by 2 (or divide by 1/2): x = 20. Check: (1/2)(20) - 4 = 10 - 4 = 6.

3. Solve: -2x + 7 = 1

x = -3

x = 3

x = 6

x = -1

Answer: x = 3. Explanation: Subtract 7: -2x = -6. Divide by -2: x = 3. Check: -2(3)+7 = -6+7 = 1.

4. Solve: 4 = 2(x - 1)

x = 2

x = 3

x = 1

x = 4

Answer: x = 3. Explanation: Divide both sides by 2: 2 = x - 1. Then add 1: x = 3. Check: 2(3-1) = 2(2) = 4.

✏️ Part 2: Short Answers — Work & Final Answers

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

Step 1: Divide both sides by 2 → x + 3 = 7 Step 2: Subtract 3 → x = 4 Check: 2(4 + 3) = 2(7) = 14 ✓

Final answer: x = 4

6. Solve: (3/4)x + 2 = 8

Step 1: Subtract 2 → (3/4)x = 6 Step 2: Multiply both sides by 4/3 → x = 6 × 4/3 = 8 Check: (3/4)(8) + 2 = 6 + 2 = 8 ✓

Final answer: x = 8

7. Word problem: Sam bought identical notebooks for $4 each and paid a $10 shipping fee. The total cost was $50. How many notebooks did Sam buy?

Let n = number of notebooks. Equation: 4n + 10 = 50 Subtract 10: 4n = 40 Divide by 4: n = 10 Check: 10×$4 + $10 = $40 + $10 = $50 ✓

Final answer: 10 notebooks

8. Solve and check: 5x - 2 = 3x + 6

Step 1: Subtract 3x from both sides → 2x - 2 = 6 Step 2: Add 2 → 2x = 8 Step 3: Divide by 2 → x = 4 Check by substitution: Left = 5(4) - 2 = 20 - 2 = 18. Right = 3(4) + 6 = 12 + 6 = 18 ✓

Final answer: x = 4

Teacher Notes: Learning Target, Supports, and Extensions

Learning target: I can solve two-step equations and check my solution by substitution.

Success criteria: 1) Undo addition/subtraction first. 2) Then undo multiplication/division. 3) Substitute solution to check equality.

Differentiation strategies: Provide step prompts, allow calculators for arithmetic, let students pair up, or use guided templates showing inverse steps.

Extension activity: Create a real-life two-step equation (money, temperature, distance). Exchange with a peer and solve a classmate's problem. Try equations with fractions or decimals.

Dyslexia-friendly options: Break instructions into short lines, highlight symbols in bold, read problems aloud on request, allow colored overlays or extra processing time.