Question

Select all the statements that are true. Explain your reasoning

4−2(3+7)=4−2⋅3−2⋅7
4−2(3+7)=4+−2⋅3+−2⋅7
4−2(3+7)=4−2⋅3+2⋅7
4−2(3+7)=4−(2⋅3+2⋅7)

Answer 1

First and second are both true.

Third and fourth are not true.

Explanation:

4−2(3+7)=4−2⋅3−2⋅7

4−2(3+7)= 4 - 2(3+7) [ -2*3 - 2*7 : the -2 can be removed from -2*3-2*7 to make -2(3 + 7); communative] This results in 4-2(3+7), the same on the left side

4−2(3+7)=4+−2⋅3+−2⋅7

The (4+-2*3+-2*7) can be written as (4-2*3-2*7) to simplify the "-+" to simply "-". That can be written as 4 - 2(3+7), the same as on the left side.

4−2(3+7)=4−2⋅3+2⋅7

The right side, 4-2*3+2*7, can be written as 4-2(3-7), which is NOT the same as on the left.

4−2(3+7)=4−(2⋅3+2⋅7)

The right side can be written as 4-2(3-7), which is not the same as on the left side.