ate: \( \qquad \) Per: \( \qquad \) Homework 6: Algebraic Prools (Day 1) ** This is a 2-page document! ** ections: Write the letter of the property of equality that justifies each statement. 1. If \( a=2 b \), then \( a-c=2 b-c \) A. Addition Property of Equality 2. \( 8 x=8 x \) B. Subtraction Property of Equality 3. \( 3(p-7)=3 p-21 \) C. Multiplication Property of Equality 4. If \( -7 k=-42 \), then \( k=6 \) D. Division Property of Equality 5. If \( m+n=15 \) and \( n=2 \). then \( m+2=15 \) E. Distributive Property 6. If \( \frac{x}{4}=-5 . x=-20 \) 7. If \( w^{2}=2 x \) and \( 2 x=y \), then \( w^{2}=y \) F. Substitution Property G. Reflexive Property H. Symmetric Property 8. If \( c-9=-1 \). then \( c=8 \) 9. If \( n=-3 \), then \( -3=n \)

If you're diving into the realm of algebra, it's fascinating to note that many of these properties of equality date back to ancient mathematicians like Euclid! His work laid the groundwork for logical deduction and reasoning that we still apply today in algebra. Understanding these properties not only helps you solve equations but also boosts your analytical skills, making you a mini mathematician of sorts! When applying properties of equality, one common mistake is misunderstanding the use of the Distributive Property. It's essential to make sure you're distributing correctly—like when you're sharing pizza! If you have 3 slices of pizza for each of the 4 friends, that's not just 3 slices, but 3 times 4 slices! Keep that in mind to avoid mix-ups when simplifying expressions!