Let's analyze the given expression step-by-step:
[tex]\[
9 + 4(x + 2) - 3x
\][/tex]
1. Identify Each Component:
- [tex]\(9\)[/tex] is a constant term.
- [tex]\(4(x + 2)\)[/tex] involves a distributive property where 4 is multiplied by both [tex]\(x\)[/tex] and 2. Here, [tex]\(x\)[/tex] is a variable, and 2 is a constant.
- [tex]\(-3x\)[/tex] means [tex]\(3\)[/tex] is multiplied by the variable [tex]\(x\)[/tex].
2. Distribute [tex]\(4\)[/tex] in [tex]\(4(x + 2)\)[/tex]:
- [tex]\(4(x + 2)\)[/tex] can be expanded to [tex]\(4x + 8\)[/tex].
So the expression becomes:
[tex]\[
9 + 4x + 8 - 3x
\][/tex]
3. Combine Like Terms:
- Combine the constant terms: [tex]\(9 + 8 = 17\)[/tex].
- Combine the terms with [tex]\(x\)[/tex]: [tex]\(4x - 3x = x\)[/tex].
So the simplified expression is:
[tex]\[
17 + x
\][/tex]
4. Focus on the Term "3" in the original expression:
In the original expression [tex]\(9 + 4(x + 2) - 3x\)[/tex], "3" appears in the term [tex]\(-3x\)[/tex]. This means that "3" is multiplied by the variable [tex]\(x\)[/tex]. In mathematics, a term that is multiplied by a variable is called a coefficient.
Therefore:
The term that best describes "3" in the given expression is:
D. coefficient
