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 expression 1 is not 1 or 2

Answer 1

To find the equivalence between the two expressions provided, let's analyze them step by step.

Given Expressions:

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

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

Simplifying Expression 1:

1. Combine like terms:
   • Add the \( k \) terms: \( k + k = 2k \)
   • Add the constant terms: \( 1 + 1 - 1 = 1 \)
2. Therefore, after simplification:
   • Expression 1: \( 2k + 1 \)

Simplifying Expression 2:

1. Combine like terms:
   • Add the \( k \) terms: \( k + k = 2k \)
   • The remaining constant is \( 1 \).
2. Therefore, after simplification:
   • Expression 2: \( 2k + 1 \)

Equivalence Check:

Now we have:

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

They are equivalent: \( 2k + 1 = 2k + 1 \)

Filling in the Blanks:

Going back to your statement about filling in the blanks for: Expression 1: \( 2k + \text{blank} - 1 \)
Expression 2: \( 2k + \text{blank} \)

Since both simplified expressions yield \( 2k + 1 \), we can determine:

• For Expression 1: The blank must be \( 2 \) because \( 2k + 2 - 1 = 2k + 1 \).
• For Expression 2: The blank must also be \( 1 \) because it needs to match \( 2k + 1 \).

Final Answer:

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

Since it was stated that Expression 1 is not 1 or 2, the blank in Expression 1 should be specifically 2 in this context.