Answer the numbers that make the algebraic expression represented by the models equivalent expression 1: k k + 1 + 1 + 1 - 1 expression 2: k k + 1 + 1 expression 1: 2 k + blank - 1 expression 2: 2 k + blank

Answer 1

To analyze the algebraic expressions represented by the models you provided, we'll start with the two expressions and attempt to identify the blanks.

Expression 1:

The first expression you provided is: \[ k + (k + 1) + 1 + 1 - 1 \]

This simplifies as follows:

1. Combine like terms:
   • \( k + k = 2k \)
   • \( 1 + 1 - 1 = 1 \)

Thus, the simplified version of Expression 1 is: \[ 2k + 1 \]

Expression 2:

The second expression is: \[ k + (k + 1) + 1 \]

Simplifying this expression:

1. Combine like terms:
   • \( k + k = 2k \)
   • \( 1 + 1 = 2 \)

Thus, the simplified version of Expression 2 is: \[ 2k + 2 \]

Filling in the Blanks

We can now fill in the blanks based on our simplifications.

1. For Expression 1, which was simplified to \( 2k + 1 \):

   • The blank corresponds to \( 1 \).

2. For Expression 2, which was simplified to \( 2k + 2 \):

   • The blank corresponds to \( 2 \).

Final Results:

• Expression 1: \( 2k + 1 \) (blank = 1)
• Expression 2: \( 2k + 2 \) (blank = 2)