Question

the equation $-6(y + 5) = 24$ is solved in several steps below. for each step, choose the reason that best justifies it.

step	reason
$\frac{-6(y + 5)}{-6} = \frac{24}{-6}$	division property of equality
$y + 5 = -4$	simplifying
$y + 5 - 5 = -4 - 5$	subtraction property of equality
$y = -9$	simplifying

Explanation:

Step1: Verify division equality step

We use the Division Property of Equality, which states that if we divide both sides of an equation by the same non-zero number, the equality holds.
$$\frac{-6(y+5)}{-6} = \frac{24}{-6}$$

Step2: Simplify to get new equation

Calculate the division on both sides to simplify the expression.
$$y+5 = -4$$

Step3: Apply subtraction equality rule

Use the Subtraction Property of Equality, which states that if we subtract the same number from both sides of an equation, the equality holds.
$$y+5-5 = -4-5$$

Step4: Simplify to find final value

Calculate the subtraction on both sides to solve for $y$.
$$y = -9$$

Answer:

The justifications for each step are correctly matched as:

1. $\boldsymbol{-6(y+5)=24}$: Given equation
2. $\boldsymbol{\frac{-6(y+5)}{-6} = \frac{24}{-6}}$: Division Property of Equality
3. $\boldsymbol{y+5=-4}$: Simplifying
4. $\boldsymbol{y+5-5=-4-5}$: Subtraction Property of Equality
5. $\boldsymbol{y=-9}$: Simplifying

The final solution to the equation is $\boldsymbol{y=-9}$