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Problem Overview:

The task is to match each statement with the appropriate property of equality. The properties listed are:

- A. Addition Property of Equality
- B. Subtraction Property of Equality
- C. Multiplication Property of Equality
- D. Division Property of Equality
- E. Distributive Property
- F. Substitution Property
- G. Reflexive Property
- H. Symmetric Property
- I. Transitive Property

Each property will be used more than once, and we need to carefully analyze each statement to determine which property it corresponds to.

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Solution:

#### 1. If \( k = 3 \), then \( 3 = k \)
- This statement shows that if two quantities are equal, their order can be reversed.
- Property: Symmetric Property
- Answer: H

#### 2. If \( 2x = 14 \), then \( x = 7 \)
- Here, both sides of the equation are divided by 2 to isolate \( x \).
- Property: Division Property of Equality
- Answer: D

#### 3. \( 4 = 4 \)
- This statement asserts that any quantity is equal to itself.
- Property: Reflexive Property
- Answer: G

#### 4. If \( -5x - 1 = -11 \), then \( -5x = -10 \)
- In this case, 1 is added to both sides of the equation to isolate the term involving \( x \).
- Property: Addition Property of Equality
- Answer: A

#### 5. If \( 10a = 2b \) and \( 2b = c \), then \( 10a = c \)
- This statement uses the fact that if two quantities are equal to a third quantity, they are equal to each other.
- Property: Transitive Property
- Answer: I

#### 6. \( -7(x - 4) = -7x + 28 \)
- Here, the distributive property is applied to expand the left-hand side.
- Property: Distributive Property
- Answer: E

#### 7. If \( 6y = 24 \), then \( 6y - 3 = 24 - 3 \)
- Both sides of the equation have 3 subtracted from them.
- Property: Subtraction Property of Equality
- Answer: B

#### 8. If \( 10x + w = 41 \) and \( w = 1 \), then \( 10x + 1 = 41 \)
- The value of \( w \) is substituted into the equation.
- Property: Substitution Property
- Answer: F

#### 9. If \( \frac{y}{2} = -10 \), then \( y = -20 \)
- Both sides of the equation are multiplied by 2 to isolate \( y \).
- Property: Multiplication Property of Equality
- Answer: C

#### 10. If \( 3x = 2y \) and \( 2y = z \), then \( 3x = z \)
- This statement uses the transitive property, as if two quantities are equal to a third quantity, they are equal to each other.
- Property: Transitive Property
- Answer: I

#### 11. If \( 7m = 35 \), then \( 7m + 4 = 35 + 4 \)
- Both sides of the equation have 4 added to them.
- Property: Addition Property of Equality
- Answer: A

#### 12. If \( -2x = 18 \), then \( 18 = -2x \)
- The order of the equality is reversed.
- Property: Symmetric Property
- Answer: H

#### 13. Given \( 3x^2 + 1 \), if \( x = 5 \), then \( 3(5)^2 + 1 \)
- The value of \( x \) is substituted into the expression.
- Property: Substitution Property
- Answer: F

#### 14. If \( m = -2 \), then \( 8m = -16 \)
- Both sides of the equation are multiplied by 8 to isolate \( 8m \).
- Property: Multiplication Property of Equality
- Answer: C

#### 15. \( 10y = 10y \)
- This statement asserts that any quantity is equal to itself.
- Property: Reflexive Property
- Answer: G

#### 16. \( 5x + 8x = x(5 + 8) \)
- The distributive property is applied to combine like terms.
- Property: Distributive Property
- Answer: E

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Final Answer:

\[
\boxed{
\begin{array}{ll}
1. & \text{H} \\
2. & \text{D} \\
3. & \text{G} \\
4. & \text{A} \\
5. & \text{I} \\
6. & \text{E} \\
7. & \text{B} \\
8. & \text{F} \\
9. & \text{C} \\
10. & \text{I} \\
11. & \text{A} \\
12. & \text{H} \\
13. & \text{F} \\
14. & \text{C} \\
15. & \text{G} \\
16. & \text{E} \\
\end{array}
}
\]