Review for Test 3: Algebraic Properties and Linear Equations

Vocabulary and conceptual flashcards covering the commutative properties of addition and multiplication, the distributive property, and solving linear equations from the Review for Test 3 problem set.

Commutative Property of Addition ($x + 8$)

The property stating that the order in which terms are added does not change the sum, allowing $x + 8$ to be rewritten as $8 + x$.

Commutative Property of Multiplication ($zx$)

The property stating that the order of factors does not affect the product, which completes the statement as $zx = xz$.

Commutative Property of Addition ($2x + 15$)

The property used to change the order of addends without altering the expression's value, completing the statement as $2x + 15 = 15 + 2x$.

Distributive Property ($8(x + y)$)

The property used to remove parentheses by multiplying the external term across each term inside, expanding $8(x + y)$ to $8x + 8y$.

Linear Equation: $-4y + 8 = -2(3y + 4)$

An algebraic equation with the single solution $y = -8$, solved by expanding the right-hand side using the distributive property to $-6y - 8$ and isolating the variable $y$.