To simplify the expression [tex]\( 7y + 3(2 - y) + 6y \)[/tex], let's break it down step by step:
1. Distribute within the parentheses:
[tex]\[
3(2 - y)
\][/tex]
Distribute [tex]\(3\)[/tex] to both [tex]\(2\)[/tex] and [tex]\(-y\)[/tex]:
[tex]\[
3 \cdot 2 - 3 \cdot y = 6 - 3y
\][/tex]
2. Substitute the distributed terms back into the original expression:
[tex]\[
7y + (6 - 3y) + 6y
\][/tex]
3. Combine all the like terms, which are the terms involving [tex]\(y\)[/tex]:
- First, combine the coefficients of [tex]\(y\)[/tex]:
[tex]\[
7y + 6y - 3y = (7 + 6 - 3)y = 10y
\][/tex]
- Then include the constant term [tex]\(6\)[/tex]:
[tex]\[
10y + 6
\][/tex]
4. Thus, after simplification, the expression becomes:
[tex]\[
10y + 6
\][/tex]
So, the final simplified expression is [tex]\(10y + 6\)[/tex].
