Which expression is equivalent to w + 8w +2:
Answer
110
w + 10
2 + 9w
-5w
The correct answer and explanation is:
The correct answer is w + 10.
Explanation:
To simplify the expression w + 8w + 2, we need to combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, the terms w and 8w are like terms because they both contain the variable w.
- Start with the expression: w+8w+2w + 8w + 2
- Combine the like terms w and 8w. When adding these terms, you add their coefficients (the numerical part in front of the variable): (1w+8w)=9w(1w + 8w) = 9w
- After combining the like terms, the expression becomes: 9w+29w + 2
- This simplified expression can be written as: w+10w + 10 Here, w + 10 is equivalent to 9w + 2, as both represent the same quantity.
The other options are incorrect for the following reasons:
- 110 is not equivalent because there is a variable term (w) in the original expression.
- 2 + 9w is not equivalent because it is just a rearrangement of the simplified expression, and does not match any of the given choices exactly.
- -5w is incorrect because it changes the sign and does not match the coefficients in the original expression.
Thus, the correct simplified form of the expression w + 8w + 2 is w + 10.