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

Answer 1

To analyze the expressions you've provided, let's break it down step by step.

Expression 1:

k + k + 1 + 1 - 1

This expression simplifies as follows:

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

So, Expression 1 simplifies to: 2k + 1

Expression 2:

k + k + 1

This expression simplifies as follows:

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

So, Expression 2 simplifies to: 2k + 1

Now let's fill in the blanks:

You stated:

• Expression 1: \( 2k + \text{blank} - 1 \)
• Expression 2: \( 2k + \text{blank} \)

From the simplification above, we can see that both simplified expression 1 and expression 2 are equal to \(2k + 1\).

The first statement can be rewritten (noting that it states expression 1 is not 1):

1. \( 2k + \text{blank} - 1 = 2k + 1 \)

   • To find the blank, we can rearrange: \[ \text{blank} - 1 = 1 \]
   • Thus, \(\text{blank} = 1 + 1 = 2\).

2. Now for expression 2 \(2k + \text{blank}\):

   • Since we want \(2k + 2\) to equal \(2k + 1\), the value of the blank here must also be: \[ \text{blank} = 1 \]

Thus, filling the blanks correctly in both cases gives us:

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

Summary

The blanks in the expressions are:

• Expression 1: 2
• Expression 2: 1