Question

are the two expressions shown below equivalent? explain.
$4(n + 3) - (3 + n)$ and $3n + 9$

Explanation:

Step1: Expand the first expression

First, we expand \(4(n + 3)-(3 + n)\). Using the distributive property \(a(b + c)=ab+ac\), we get \(4n+12 - 3 - n\).

Step2: Combine like terms

Combine the like terms \(4n - n\) and \(12 - 3\). So \(4n - n=3n\) and \(12 - 3 = 9\). Then the first expression simplifies to \(3n+9\).

Step3: Compare the two expressions

The second expression is \(3n + 9\). Since the simplified form of the first expression is also \(3n + 9\), the two expressions are equivalent.

Answer:

Yes, the two expressions \(4(n + 3)-(3 + n)\) and \(3n + 9\) are equivalent because when we expand and simplify \(4(n + 3)-(3 + n)\), we get \(3n + 9\) which is the same as the second expression.