To simplify the given algebraic expression [tex]\(3 - 4y - 3y - y + 6\)[/tex] fully, follow these steps:
1. Combine the constants:
- Identify the constant terms in the expression. Here they are [tex]\(3\)[/tex] and [tex]\(6\)[/tex].
[tex]\[
3 + 6
\][/tex]
- Add these constants together:
[tex]\[
3 + 6 = 9
\][/tex]
2. Combine the [tex]\(y\)[/tex] terms:
- Identify the terms that contain [tex]\(y\)[/tex] in the expression. Here they are [tex]\(-4y\)[/tex], [tex]\(-3y\)[/tex], and [tex]\(-y\)[/tex].
- Combine these like terms by adding their coefficients:
[tex]\[
-4y - 3y - y
\][/tex]
- Calculate the sum of the coefficients:
[tex]\[
-4 - 3 - 1 = -8
\][/tex]
So,
[tex]\[
-4y - 3y - y = -8y
\][/tex]
3. Combine the constant term and the [tex]\(y\)[/tex] term:
- Now, combine the constant [tex]\(9\)[/tex] and the [tex]\(y\)[/tex] term [tex]\(-8y\)[/tex] to obtain the simplified expression:
[tex]\[
9 - 8y
\][/tex]
Therefore, the fully simplified expression is:
[tex]\[
9 - 8y
\][/tex]
