To determine which of the given expressions are equal to [tex]\((3 \cdot 7) - 2\)[/tex], let's carefully evaluate each one step-by-step.
First, we need to calculate the value of the original expression [tex]\((3 \cdot 7) - 2\)[/tex]:
[tex]\[
(3 \cdot 7) - 2 = 21 - 2 = 19
\][/tex]
Now, let's evaluate each of the given expressions and compare them to 19.
### Expression A:
[tex]\[
2 - (3 \cdot 7)
\][/tex]
Calculate the value inside the parentheses first:
[tex]\[
3 \cdot 7 = 21
\][/tex]
Then, perform the subtraction:
[tex]\[
2 - 21 = -19
\][/tex]
Expression A evaluates to [tex]\(-19\)[/tex], which is not equal to 19.
### Expression B:
[tex]\[
3 \cdot (7 - 2)
\][/tex]
Calculate the value inside the parentheses first:
[tex]\[
7 - 2 = 5
\][/tex]
Then, perform the multiplication:
[tex]\[
3 \cdot 5 = 15
\][/tex]
Expression B evaluates to 15, which is not equal to 19.
### Expression C:
[tex]\[
(7 \cdot 3) - 2
\][/tex]
Calculate the value inside the parentheses first:
[tex]\[
7 \cdot 3 = 21
\][/tex]
Then, perform the subtraction:
[tex]\[
21 - 2 = 19
\][/tex]
Expression C evaluates to 19, which is equal to the original expression's value of 19.
### Expression D:
[tex]\[
(3 - 2) \cdot (7 - 2)
\][/tex]
Calculate the values inside the parentheses first:
[tex]\[
3 - 2 = 1
\][/tex]
[tex]\[
7 - 2 = 5
\][/tex]
Then, perform the multiplication:
[tex]\[
1 \cdot 5 = 5
\][/tex]
Expression D evaluates to 5, which is not equal to 19.
In conclusion, the only expression that is equal to the original expression [tex]\((3 \cdot 7) - 2\)[/tex] is:
C. [tex]\((7 \cdot 3) - 2\)[/tex]
