Certainly! Let's understand what the phrase "twice the weight of the trout" means, and translate it step-by-step into an algebraic expression.
1. Let \( w \) be the weight of the trout. This is our variable.
2. The phrase "twice the weight" of something means multiplying that weight by 2.
Now let's look at the options provided and see which one correctly represents "twice the weight of the trout":
- Option A: \( w + 2 \). This represents the weight of the trout plus 2, not twice the weight.
- Option B: \( w - 2 \). This represents the weight of the trout minus 2, not twice the weight.
- Option C: \( \frac{w}{2} \). This represents half the weight of the trout, not twice the weight.
- Option D: \( 2w \). This correctly represents twice the weight of the trout, since multiplying by 2 gives us "twice."
Thus, the correct algebraic expression representing "twice the weight of the trout" is:
[tex]\[ 2w \][/tex]
So, the correct answer is:
[tex]\[ \boxed{D} \][/tex]
