Question

the expression $8 + 3(4 + w)$ is simplified in several steps below. for each step, choose the reason that best justifies it. step reason $8 + 3(4 + w)$ given expression $8 + 12 + 3w$ select $20 + 3w$ select $3w + 20$ select

Explanation:

Step1: Identify the first step's reason

To get from \(8 + 3(4 + w)\) to \(8 + 12 + 3w\), we use the Distributive Property. The Distributive Property states that \(a(b + c)=ab+ac\). Here, \(a = 3\), \(b = 4\), and \(c = w\), so \(3(4 + w)=3\times4+3\times w = 12 + 3w\).

Step2: Identify the second step's reason

To get from \(8 + 12 + 3w\) to \(20 + 3w\), we combine the like terms \(8\) and \(12\). Combining like terms (addition of constants here) gives \(8+12 = 20\).

Step3: Identify the third step's reason

To get from \(20 + 3w\) to \(3w + 20\), we use the Commutative Property of Addition. The Commutative Property of Addition states that \(a + b=b + a\), so \(20+3w = 3w + 20\).

Answer:

• For \(8 + 12 + 3w\): Distributive Property
• For \(20 + 3w\): Combine like terms (or Addition of real numbers)
• For \(3w + 20\): Commutative Property of Addition