Let's go through each problem step by step:

13. If $x + 7 = 23$, then $x = 16$.

• Solution: Subtract 7 from both sides to isolate $x$: $x + 7 - 7 = 23 - 7 \implies x = 16.$
• Property Used: Subtraction Property of Equality.

14. If $4x = 40$, then $x = 10$.

• Solution: Divide both sides by 4 to isolate $x$: $\frac{4x}{4} = \frac{40}{4} \implies x = 10.$
• Property Used: Division Property of Equality.

15. If $x = 7$ and $y = 7$, then $x = y$.

• Solution: Both $x$ and $y$ are equal to the same value, 7, so $x = y$.
• Property Used: Transitive Property of Equality.

16. If $4x = 28$, then $28 = 4x$.

• Solution: This is simply rewriting the equation with the terms swapped.
• Property Used: Symmetric Property of Equality (since $a = b \implies b = a$).

17. If $x - 24 = 25$, then $x = 49$.

• Solution: Add 24 to both sides to isolate $x$: $x - 24 + 24 = 25 + 24 \implies x = 49.$
• Property Used: Addition Property of Equality.

Let me know if you want further details or have any questions!

Related Questions:

1. What is the Addition Property of Equality, and how is it applied in problem-solving?
2. Can you give more examples of the Transitive Property of Equality in algebra?
3. How does the Symmetric Property of Equality help in equation manipulation?
4. Why is it necessary to perform the same operation on both sides of an equation?
5. What are other properties of equality used in solving linear equations?

Tip:

Always check your final answer by plugging it back into the original equation to ensure correctness!