Question

Select the correct choices to complete the sentence.
Evaluate the expression. Name the property used in each step.



2(3⋅2−5)+3⋅13




=2(6−5)+3⋅13
1 of 5.
Substitution
=2(1)+3⋅13
2 of 5.
Substitution
=2+3⋅13
3 of 5.
Multiplicative Identity
=2+1
4 of 5.
Select Choice
=3
5 of 5.
Select Choice

Answer 1

Let's evaluate the expression step-by-step and identify the property used in each step.

Given expression:
\[ 2(3 \cdot 2 - 5) + 3 \cdot 13 \]

### Step 1
First, we rewrite the expression using the distributive property to evaluate \( 3 \cdot 2 - 5 \):

\[ = 2(6 - 5) + 3 \cdot 13 \]
**Property used:** Substitution

### Step 2
Next, we simplify \( 6 - 5 \):

\[ = 2(1) + 3 \cdot 13 \]
**Property used:** Substitution

### Step 3
Then, we evaluate \( 2(1) \):

\[ = 2 + 3 \cdot 13 \]
**Property used:** Multiplicative Identity (because multiplying by 1 does not change the value)

### Step 4
Now, calculate \( 3 \cdot 13 \):

\[ = 2 + 39 \]
**Property used:** Multiplication

### Step 5
Finally, add \( 2 + 39 \):

\[ = 41 \]
**Property used:** Addition

So, in summary:

1. \( 2(3 \cdot 2 - 5) + 3 \cdot 13 = 2(6 - 5) + 3 \cdot 13 \) (Substitution)
2. \( 2(6 - 5) + 3 \cdot 13 = 2(1) + 3 \cdot 13 \) (Substitution)
3. \( 2(1) + 3 \cdot 13 = 2 + 3 \cdot 13 \) (Multiplicative Identity)
4. \( 2 + 3 \cdot 13 = 2 + 39 \) (Multiplication)
5. \( 2 + 39 = 41 \) (Addition)

So the final result is \( 41 \), and the properties used are identified accordingly.