Which expression is equivalent to $9 x-3 y-5 x+7 y+x+y ?$
A) $10 x y$
B) $4 x+4 y$
C) $5 x+5 y$
D) $5 x^2+4 y^2$
Answer (1)
Combine the x terms: 9 x − 5 x + x = 5 x .
Combine the y terms: − 3 y + 7 y + y = 5 y .
Write the simplified expression: 5 x + 5 y .
The equivalent expression is 5 x + 5 y .
Explanation
Understanding the Problem We are asked to find an expression equivalent to 9 x − 3 y − 5 x + 7 y + x + y . This involves combining like terms, which means grouping the x terms together and the y terms together.
Combining x terms First, let's group the x terms: 9 x − 5 x + x . We can rewrite this as ( 9 − 5 + 1 ) x . Now, let's simplify the coefficient: 9 − 5 + 1 = 5 . So, the x terms simplify to 5 x .
Combining y terms Next, let's group the y terms: − 3 y + 7 y + y . We can rewrite this as ( − 3 + 7 + 1 ) y . Now, let's simplify the coefficient: − 3 + 7 + 1 = 5 . So, the y terms simplify to 5 y .
Final Expression Now, we combine the simplified x and y terms: 5 x + 5 y . This is the simplified expression.
Identifying the Correct Option Comparing our simplified expression 5 x + 5 y with the given choices, we see that it matches option C. Therefore, the equivalent expression is 5 x + 5 y .
Examples
Imagine you are managing inventory for a small business. You start with 9 boxes of product A, sell 5 boxes, receive 1 more box, sell 3 boxes of product B, receive 7 boxes, and then receive 1 more box. Simplifying expressions like this helps you quickly determine your final inventory levels for each product.
