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 | addition property of equality
\frac{-8(y - 1)}{-8} = \frac{-40}{-8} | subtraction property of equality, multiplication property of equality, division property of equality
y - 1 = 5 |
y - 1 + 1 = 5 + 1 | simplifying, distributive property
y = 6 | \choose one\

Explanation:

Step 1: Analyze the first step (division)

The first step is dividing both sides of \(-8(y - 1)=-40\) by \(-8\). The Division Property of Equality states that if \(a = b\) and \(c
eq0\), then \(\frac{a}{c}=\frac{b}{c}\). So this step uses the Division Property of Equality.

Step 2: Analyze the second step (simplifying)

After dividing, \(\frac{-8(y - 1)}{-8}=\frac{-40}{-8}\) simplifies to \(y - 1 = 5\). This is just simplifying the fractions, so the reason is Simplifying.

Step 3: Analyze the third step (addition)

The step \(y-1 + 1=5 + 1\) adds \(1\) to both sides. The Addition Property of Equality states that if \(a = b\), then \(a + c=b + c\). So this step uses the Addition Property of Equality.

Step 4: Analyze the fourth step (simplifying)

The step \(y-1 + 1=5 + 1\) simplifies to \(y = 6\) (since \(-1+1 = 0\) and \(5 + 1=6\)). This is simplifying the left - hand side (combining like terms) and the right - hand side, so the reason is Simplifying.

Now, let's match each step with the correct reason:

1. For \(-8(y - 1)=-40\) to \(\frac{-8(y - 1)}{-8}=\frac{-40}{-8}\): Reason is Division Property of Equality.
2. For \(\frac{-8(y - 1)}{-8}=\frac{-40}{-8}\) to \(y - 1 = 5\): Reason is Simplifying.
3. For \(y - 1 = 5\) to \(y-1 + 1=5 + 1\): Reason is Addition Property of Equality.
4. For \(y-1 + 1=5 + 1\) to \(y = 6\): Reason is Simplifying.

Answer:

• Step \(-8(y - 1)=-40\) to \(\frac{-8(y - 1)}{-8}=\frac{-40}{-8}\): Division Property of Equality
• Step \(\frac{-8(y - 1)}{-8}=\frac{-40}{-8}\) to \(y - 1 = 5\): Simplifying
• Step \(y - 1 = 5\) to \(y-1 + 1=5 + 1\): Addition Property of Equality
• Step \(y-1 + 1=5 + 1\) to \(y = 6\): Simplifying