Question

select the expressions that are equivalent to 3(-2n - 4) + 9. -2n - 3 -3n - 6 3(-7n + 5n - 4) + 9 -6n - 3

Explanation:

Step1: Simplify the original expression

First, we expand the term \(3(-2n - 4)\) using the distributive property \(a(b + c)=ab+ac\). Here, \(a = 3\), \(b=-2n\) and \(c = - 4\). So we have:
\(3\times(-2n)+3\times(-4)=-6n-12\)
Then we add 9 to this result:
\(-6n - 12+9=-6n-3\)

Step2: Analyze the third option

For the expression \(3(-7n + 5n-4)+9\), first we simplify the terms inside the parentheses: \(-7n + 5n=-2n\), so the expression inside the parentheses becomes \(-2n-4\). Then we have \(3(-2n - 4)+9\), which is the original expression, so it is equivalent.

Step3: Analyze the other options

• For \(-2n-3\): The coefficient of \(n\) is \(- 2\) while in our simplified original expression the coefficient of \(n\) is \(-6\), so it is not equivalent.
• For \(-3n - 6\): The coefficient of \(n\) is \(-3\) and the constant term is \(-6\), which is different from our simplified expression \(-6n-3\), so it is not equivalent.

Answer:

The equivalent expressions are \(3(-7n + 5n - 4)+9\) and \(-6n - 3\)