To determine which expression is equivalent to [tex]\(9x - 3y - 5x + 7y + x + y\)[/tex], let's simplify the given expression step-by-step.
1. Combine like terms:
First, collect all the [tex]\(x\)[/tex] terms together and all the [tex]\(y\)[/tex] terms together.
[tex]\[
(9x - 5x + x) + (-3y + 7y + y)
\][/tex]
2. Simplify the [tex]\(x\)[/tex] terms:
[tex]\[
9x - 5x + x = (9 - 5 + 1)x = 5x
\][/tex]
3. Simplify the [tex]\(y\)[/tex] terms:
[tex]\[
-3y + 7y + y = (-3 + 7 + 1)y = 5y
\][/tex]
4. Combine the simplified terms:
[tex]\[
5x + 5y
\][/tex]
Therefore, the expression equivalent to [tex]\(9x - 3y - 5x + 7y + x + y\)[/tex] is:
[tex]\[
5x + 5y
\][/tex]
So, the correct answer is:
A) [tex]\(5 x + 5 y\)[/tex]
