To determine which of the given expressions are equivalent to [tex]\((4 \cdot 1) - 6\)[/tex], we must evaluate both the original expression and each option. Let's go through each step-by-step.
Firstly, let's evaluate the original expression:
[tex]\[
(4 \cdot 1) - 6
\][/tex]
[tex]\[
4 - 6 = -2
\][/tex]
We need to determine if any of the options A, B, C, or D also result in [tex]\(-2\)[/tex].
### Option A: [tex]\((4 \div 1) - 6\)[/tex]
Evaluate the expression:
[tex]\[
(4 \div 1) - 6
\][/tex]
[tex]\[
4 - 6 = -2
\][/tex]
This matches the original expression.
### Option B: [tex]\((1 \cdot 4) - 6\)[/tex]
Evaluate the expression:
[tex]\[
(1 \cdot 4) - 6
\][/tex]
[tex]\[
4 - 6 = -2
\][/tex]
This also matches the original expression.
### Option C: [tex]\(4 \cdot (1 - 6)\)[/tex]
Evaluate the expression:
[tex]\[
4 \cdot (1 - 6)
\][/tex]
[tex]\[
4 \cdot (-5) = -20
\][/tex]
This does not match the original expression.
### Option D: [tex]\(6 - (1 \cdot 4)\)[/tex]
Evaluate the expression:
[tex]\[
6 - (1 \cdot 4)
\][/tex]
[tex]\[
6 - 4 = 2
\][/tex]
This does not match the original expression.
Based on our evaluations, the expressions that are equivalent to the original [tex]\((4 \cdot 1) - 6\)[/tex] are:
- (A) [tex]\((4 \div 1) - 6\)[/tex]
- (B) [tex]\((1 \cdot 4) - 6\)[/tex]
Thus, the correct answers are:
A and B
