Use the image to answer the question.

Question

An illustration shows one tall rectangular tile equals x, another tall rectangular tile equals y, a square tile equals positive 1, and another square tile equals negative 1.

Model each pair of algebraic expressions using the key. Which of the following are not equivalent expressions?

(1 point)
Responses

x+3+3y
and x+3(1+y)
x plus 3 plus 3 y and x plus 3 left parenthesis 1 plus y right parenthesis

2(x−1)+y
and 2x+y−2
2 left parenthesis x minus 1 right parenthesis plus y and 2 x plus y minus 2

x+4+y
and 4x+y
x plus 4 plus y and 4 x plus y

x+4+y
and x+5+y−1

Answer 1

To determine which pairs of algebraic expressions are not equivalent, we will simplify each pair.

1. For the expressions \(x + 3 + 3y\) and \(x + 3(1 + y)\):

   • \(x + 3 + 3y\) is already simplified.
   • \(x + 3(1 + y) = x + 3 + 3y\).

   Both expressions are equivalent.

2. For the expressions \(2(x - 1) + y\) and \(2x + y - 2\):

   • \(2(x - 1) + y = 2x - 2 + y\).
   • \(2x + y - 2\) is already \(2x + y - 2\).

   Both expressions are equivalent.

3. For the expressions \(x + 4 + y\) and \(4x + y\):

   • \(x + 4 + y\) cannot be simplified to equal \(4x + y\).

   These expressions are not equivalent.

4. For the expressions \(x + 4 + y\) and \(x + 5 + y - 1\):

   • \(x + 5 + y - 1 = x + 4 + y\).

   Both expressions are equivalent.

Conclusion:

The pair of expressions that are not equivalent is:

\(x + 4 + y\) and \(4x + y\).