Question
3hich expression is equivalent to \( 3(2 x+4 y)-y \) ? A \( 17 x y \) B \( 6 x+12 \) C \( 3(6 x y)-y \) D \( 6(x+2 y)-y \)
Ask by Warner Nichols. in the United States
Mar 08,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The expression equivalent to \(3(2x + 4y) - y\) is \(6x + 11y\), which matches option D.
Solution
\[
3(2x+4y)-y
\]
1. Distribute the \(3\) over each term in the parentheses:
\[
3(2x) + 3(4y) = 6x + 12y
\]
2. Subtract \(y\):
\[
6x + 12y - y = 6x + 11y
\]
3. Recognize that the expression in option D is:
\[
6(x+2y)-y = 6x + 12y - y = 6x + 11y
\]
Thus, the correct answer is option D.
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Simplify this solution Mind Expander
To simplify the expression \( 3(2x + 4y) - y \), first distribute the 3: \[ 3(2x) + 3(4y) - y = 6x + 12y - y \] Now, combine like terms: \[ 6x + 12y - y = 6x + 11y \] Now let's look at the options provided. Option D, \( 6(x + 2y) - y \), can be further examined. Distributing the 6: \[ 6(x) + 6(2y) - y = 6x + 12y - y = 6x + 11y \] Thus, option D represents the same expression as our simplified form. The equivalent expression is: **Answer: D**
