Question

the equation $-8(x + 1) = -40$ is solved in several steps below. for each step, choose the reason that best justifies it. your answer step reason $-8(x + 1) = -40$ given equation $\frac{-8(x + 1)}{-8} = \frac{-40}{-8}$ choose one $x + 1 = 5$ choose one $x + 1 - 1 = 5 - 1$ choose one $x = 4$ choose one

Explanation:

Step1: Identify the first step's reason

The step \(\frac{-8(x + 1)}{-8}=\frac{-40}{-8}\) involves dividing both sides of the equation \(-8(x + 1)=-40\) by \(-8\). The reason for this is the Division Property of Equality, which states that if \(a = b\) and \(c
eq0\), then \(\frac{a}{c}=\frac{b}{c}\).

Step2: Identify the second step's reason

After dividing, we get \(x + 1 = 5\). This is because when we simplify \(\frac{-8(x + 1)}{-8}\), the \(-8\) in the numerator and denominator cancels out (simplifying the fraction), and \(\frac{-40}{-8}=5\). So this is just Simplification (performing the division operation).

Step3: Identify the third step's reason

The step \(x + 1-1 = 5 - 1\) involves subtracting \(1\) from both sides of the equation \(x + 1 = 5\). The reason for this is the Subtraction Property of Equality, which states that if \(a = b\), then \(a - c = b - c\).

Step4: Identify the fourth step's reason

After subtracting \(1\) from both sides, we get \(x = 4\). This is because \(x+1 - 1=x\) (the \(+1\) and \(-1\) cancel out) and \(5 - 1 = 4\). So this is Simplification (performing the subtraction operation).

Answer:

• For \(\frac{-8(x + 1)}{-8}=\frac{-40}{-8}\): Division Property of Equality
• For \(x + 1 = 5\): Simplification (from dividing \(\frac{-8(x + 1)}{-8}\) and \(\frac{-40}{-8}\))
• For \(x + 1-1 = 5 - 1\): Subtraction Property of Equality
• For \(x = 4\): Simplification (from subtracting \(1\) on both sides)