Using both the Commutative and Associate Properties, determine whether the following two expressions are equivalent:

To determine whether the given expressions are equivalent using the Commutative and Associative Properties, let's simplify Expression 1 step by step.

**Expression 1**: \((3b + 1) + 10b + 9\)

1. **Grouping the terms**: We can rearrange the terms using the Commutative Property, which states that the order of addition does not matter.

\[
(3b + 10b + 1 + 9)
\]

2. **Associative Property**: Next, we can group the terms to make it easier to add:

\[
(3b + 10b) + (1 + 9)
\]

3. **Adding the coefficients of \(b\)**:

\[
3b + 10b = 13b
\]

4. **Adding the constants**:

\[
1 + 9 = 10
\]

So now we combine everything:

\[
13b + 10
\]

Now **Expression 1** becomes \(13b + 10\).

**Expression 2** is given as \(13b + 9\).

Now let's compare:

- Expression 1: \(13b + 10\)
- Expression 2: \(13b + 9\)

Since \(13b + 10\) is not equal to \(13b + 9\), we conclude that:

**The two expressions are not equivalent.**