Use the image to answer the question.

Question

An illustration shows two groups of tiles. One group is labeled above as Expression 1 and the other is labeled Expression 2. Expression 1 shows 2 tall rectangular tiles labeled k, 3 stacked square tiles labeled, each labeled plus 1, and one more square tile labeled negative 1. Expression 2 shows 2 tall rectangular tiles labeled k and 2 stacked square tiles labeled, both labeled plus 1.

Enter the numbers that make the algebraic expressions represented by the models equivalent.

(1 point)
Expression 1: 2k+
−1

Expression 2: 2k+

Answer 1

To express the two algebraic expressions represented by the models as equivalent, we analyze the contents of each expression.

For Expression 1:

• There are 2 tall rectangular tiles labeled \( k \) contributing \( 2k \).
• There are 3 stacked square tiles labeled \( +1 \), contributing \( +3 \).
• There is 1 square tile labeled \( -1 \), contributing \( -1 \).

So, Expression 1 can be summed up as: \[ 2k + 3 + (-1) = 2k + 2 \]

For Expression 2:

• There are 2 tall rectangular tiles labeled \( k \), contributing \( 2k \).
• There are 2 stacked square tiles labeled \( +1 \), contributing \( +2 \).

So, Expression 2 can be summed up as: \[ 2k + 2 \]

Now, we can see that both expressions equal \( 2k + 2 \).

Thus, to make the algebraic expressions represented by the models equivalent:

Expression 1: \( 2k + 2 \) Expression 2: \( 2k + 2 \)

The answer is essentially the number that completes the expressions equivalently, which is 2 for the second expression.