Question

6.The expressions 5 + 2(x –7) and 5 +2x –14are equivalent by the

A.identity property.

C.associative property of multiplication.

B.distributive property.

D.commutative property of multiplication.


7.By what property are x + 3(7 –x) and x + 21 –3x equivalent?

A.identity property

C.associative property

B.distributive property

D.commutative property

Answer 1

6) Option B) distributive property is correct

Therefore 5+2(x-7)=5+2x-14 are equivalent by using distributive property

7) Option B) distributive property is correct

Therefore x+3(7-x)=x+21-3x are equivalent by using distributive property

Explanation:

6) Given that the expressions 5+2(x-7) and 5+2x-14 are equivalent

To verify that the given expressions are equivalent by which property :

5+2(x-7)

=5+2(x)+2(-7) ( by using the distributive property a(x+y)=ax+ay )

=5+2x-14

Therefore 5+2(x-7)=5+2x-14 are equivalent by using distributive property

Therefore option B) distributive property is correct

7) Given that the expressions x+3(7-x) and x+21-3x are equivalent

To verify that the given expressions are equivalent by which property :

x+3(7-x)

=x+3(7)+3(-x) ( by using the distributive property a(x+y)=ax+ay )

=x+21-3x

Therefore x+3(7-x)=x+21-3x are equivalent by using distributive property

Therefore option B) distributive property is correct