To determine which of the given expressions is equivalent to [tex]\(2w\)[/tex], we will evaluate each one step-by-step:
1. Expression 1: [tex]\( w + w \)[/tex]
- Combine the terms: [tex]\( w + w = 2w \)[/tex]
- Result: [tex]\(2w\)[/tex]
2. Expression 2: [tex]\( 2w + w \)[/tex]
- Combine the terms: [tex]\( 2w + w = 3w \)[/tex]
- Result: [tex]\(3w\)[/tex]
3. Expression 3: [tex]\( 2w - w \)[/tex]
- Simplify the expression: [tex]\( 2w - w = w \)[/tex]
- Result: [tex]\(w\)[/tex]
4. Expression 4: [tex]\( w + 2 \)[/tex]
- This expression can't be simplified further in a way that combines terms properly, as it involves both a variable and a constant: [tex]\( w + 2 \)[/tex]
- Result: [tex]\(w + 2\)[/tex]
After evaluating all the expressions, we find that the only expression that is exactly equivalent to [tex]\(2w\)[/tex] is:
[tex]\[ w + w \][/tex]
Thus, the correct expression equivalent to [tex]\(2w\)[/tex] is [tex]\( w + w \)[/tex].
