Question

Enter the numbers that make the algebraic expressions represented by the models equivalent.
Expression 1: (x+3)
Expression 2: 2x +

Answer 1

To make the two expressions equivalent, we need to determine what the second expression, \(2x + \_\_\_\_\), should be equal to.

Given:
1. Expression 1: \(x + 3\)
2. Expression 2: \(2x + \_\_\_\_\)

To find what goes in the blank, we'll set the two expressions equal to each other:

\[
x + 3 = 2x + b
\]

Where \(b\) is the number we need to find.

To solve for \(b\), we'll isolate it:

1. Subtract \(x\) from both sides:

\[
3 = 2x - x + b
\]

This simplifies to:

\[
3 = x + b
\]

2. Now, solve for \(b\):

\[
b = 3 - x
\]

So, the number that makes the two expressions equivalent depends on the value of \(x\). There isn't a single number that will work for all values of \(x\), but rather \(b\) can be expressed as \(3 - x\).

You could substitute a value for \(x\) to get specific numbers if desired.