Answer:
1. Teresa's expression s not equivalent because she did not multiply -7 and -4 correctly.
2. Bernette's expression is not an equivalent because she should multiply before subtracting.
3. Lucy's expression is equivalent because she distributed correctly.
Step-by-step explanation:
By definition, equivalent expression have the same value but they look different.
You can find equivalent expressions of any expression by simplifying.
In this case you have the following expression:
![2-7(3x-4)](https://tex.z-dn.net/?f=2-7%283x-4%29)
Then, you know that:
1. Teresa's answer is:
![2-21x-28](https://tex.z-dn.net/?f=2-21x-28)
This is not an equivalent expression , because she did not multiply -7 and -4 correctly.
Remember that:
![(+)(+)=+\\(-)(+)=-\\(-)(-)=+](https://tex.z-dn.net/?f=%28%2B%29%28%2B%29%3D%2B%5C%5C%28-%29%28%2B%29%3D-%5C%5C%28-%29%28-%29%3D%2B)
2. Bernette's answer is:
![-5(3x-4)](https://tex.z-dn.net/?f=-5%283x-4%29)
This is not an equivalent expression, because she should multiply before subtracting (She should apply the procedure Teresa applied)
3. Lucy's answer is:
![2-21x+28](https://tex.z-dn.net/?f=2-21x%2B28)
This is an equivalent expression , because she distributed correctly (She multiplied each term inside the parentheses by -7)
Therefore, you can find an equivalent expression for the given expression by applying the Distributive property. Then:
![2-7(3x-4)=2+(-7)(3x)+(-7)(-4)=2-21x+28](https://tex.z-dn.net/?f=2-7%283x-4%29%3D2%2B%28-7%29%283x%29%2B%28-7%29%28-4%29%3D2-21x%2B28)