Algebra Proofs Practice Worksheet

I'll help you fill in the reasons for each algebra proof. Let me work through each problem carefully.

Problem 1: Given 2x - 10 = 20, Prove x = 15

Let me trace through each step:
1. 2x - 10 = 20 → This is given
2. 2x - 10 + 10 = 20 + 10 → Adding 10 to both sides (Addition Property of Equality)
3. 2x = 30 → Simplifying (combining like terms)
4. 2x/2 = 30/2 → Dividing both sides by 2 (Division Property of Equality)
5. x = 15 → Simplifying

Problem 2: Given x/2 + 5 = 12, Prove x = 14

Let me trace through each step:
1. x/2 + 5 = 12 → This is given
2. x/2 + 5 - 5 = 12 - 5 → Subtracting 5 from both sides (Subtraction Property of Equality)
3. x/2 = 7 → Simplifying
4. x/2 · 2 = 7 · 2 → Multiplying both sides by 2 (Multiplication Property of Equality)
5. x = 14 → Simplifying

Problem 3: Given 4(x + 3) = 16, Prove x = 1

Let me trace through each step:
1. 4(x + 3) = 16 → This is given
2. 4x + 12 = 16 → Distributive Property
3. 4x + 12 - 12 = 16 - 12 → Subtracting 12 from both sides (Subtraction Property of Equality)
4. 4x = 4 → Simplifying
5. 4x/4 = 4/4 → Dividing both sides by 4 (Division Property of Equality)
6. x = 1 → Simplifying

Now let me verify my answers are correct:

Problem 1 verification: If x = 15, then 2(15) - 10 = 30 - 10 = 20 ✓

Problem 2 verification: If x = 14, then 14/2 + 5 = 7 + 5 = 12 ✓

Problem 3 verification: If x = 1, then 4(1 + 3) = 4(4) = 16 ✓

All solutions check out!

Final Answer:

Problem 1 Reasons:
1. Given
2. Addition Property of Equality
3. Simplify
4. Division Property of Equality
5. Simplify

Problem 2 Reasons:
1. Given
2. Subtraction Property of Equality
3. Simplify
4. Multiplication Property of Equality
5. Simplify

Problem 3 Reasons:
1. Given
2. Distributive Property
3. Subtraction Property of Equality
4. Simplify
5. Division Property of Equality
6. Simplify