Question

the equation -8(y - 1) = -40 is solved in several steps below. for each step, choose the reason that best justifies it.
step | reason
-8(y - 1) = -40 | given equation
\\(\frac{-8(y - 1)}{-8} = \frac{-40}{-8}\\) | division property of equality
\\(y - 1 = 5\\) | simplifying
\\(y - 1 + 1 = 5 + 1\\) | \choose one\ (options: addition property of equality, subtraction property of equality, multiplication property of equality, division property of equality, simplifying, distributive property)
\\(y = 6\\) | not fully shown

Explanation:

To solve for \( y \) in the equation \( -8(y - 1)=-40 \), we follow these steps:

1. Given Equation: \( -8(y - 1)=-40 \)
2. Division Property of Equality: We divide both sides by \( -8 \) to isolate the term with \( y \):

\( \frac{-8(y - 1)}{-8}=\frac{-40}{-8} \)

1. Simplifying: After dividing, we get \( y - 1 = 5 \)
2. Addition Property of Equality: To solve for \( y \), we add \( 1 \) to both sides of the equation \( y - 1 = 5 \):

\( y - 1 + 1 = 5 + 1 \)
This step uses the Addition Property of Equality, which states that if we add the same number to both sides of an equation, the two sides remain equal.

1. Simplifying: After adding, we get \( y = 6 \)

Answer:

Addition Property of Equality