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

Question

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

Expression 2: 13b +9
(1 point)

Answer 1

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.