Question

problem 5
9 when solving $x^2 + 6x = -8$ for $x$, a student wrote $x^2 + 6x + 8 = 0$ as their first step. which property justifies this step?

1. associative property
2. commutative property
3. zero property of addition
4. addition property of equality

Explanation:

The student transformed $x^2 + 6x = -8$ to $x^2 + 6x + 8 = 0$ by adding 8 to both sides of the equation. The addition property of equality states that if you add the same value to both sides of an equation, the equality still holds. The associative property applies to grouping of operations, the commutative property applies to order of operations, and the zero property of addition refers to adding 0 to a number, none of which match this step.

Answer:

1. addition property of equality