Question

Use the distributive property to match equivalent expressions.

Answer 1

7 (-4 - x) --> -28 - 7x

7 (4 + x) --> 28 + 7x

-7 (-4 + x) --> 28 - 7x

-7 (4 - x) --> -28 + 7x

edge2021 :)

Answer 2

By using the distributive property the matched equivalent expressions are

1) -7(-4+x) =28-7x

2) -7(4-x) =-28+7x

3) 7(4+x) =28+7x

4) 7(-4-x) =-28-7x

Explanation:

Given that by using the distributive property to match the given equivalent expressions.

1) Given expression is -7(-4+x)

By Distributive property a(b+c)=ab+ac

-7(-4+x) =(-7)(-4)+(-7)(x)

=28-7x

∴ -7(-4+x) =28-7x

2) Given expression is -7(4-x)

By Distributive property a(b+c)=ab+ac

-7(4-x) =(-7)(4)+(-7)(-x)

=-28+7x

∴ -7(4-x) =-28+7x

3) Given expression is 7(4+x)

By Distributive property a(b+c)=ab+ac

7(4+x) =(7)(4)+(7)(x)

=28+7x

∴ 7(4+x) =28+7x

4) Given expression is 7(-4-x)

By Distributive property a(b+c)=ab+ac

7(-4-x) =(7)(-4)+(7)(-x)

=-28-7x

∴ 7(-4-x) =-28-7x

Hence the matched equivalent expressions are

1) -7(-4+x) =28-7x

2) -7(4-x) =-28+7x

3) 7(4+x) =28+7x

4) 7(-4-x) =-28-7x