Which expressions are equivalent to - 90 - 60w

A : - 30 (3+2w)

B : (-9-6w) ⋅ 10

C : - 3 (30 - 20w)

D : (6 + 4w) * 15

E : - 20 (4.5 + 3w)

A : - 30 (3+2w)

B : (-9-6w) ⋅ 10

E : - 20 (4.5 + 3w)

Step-by-step explanation:

Using distributive property:

A : - 30 (3+2w) = - 90 - 60w : equivalent to - 90 - 60w

B : (-9-6w) ⋅ 10 = - 90 - 60w : equivalent to - 90 - 60w

C : - 3 (30 - 20w) = - 90 + 60w : NOT equivalent to - 90 - 60w

D : (6 + 4w) * 15 = 90 + 60w : NOT equivalent to - 90 - 60w

E : - 20 (4.5 + 3w) = - 90 - 60w : equivalent to - 90 - 60w

Answer:

A : - 30 (3+2w)

B : (-9-6w) ⋅ 10

E : - 20 (4.5 + 3w)

A, B and E.

Step-by-step explanation:

We have - 90-60w. Both 90 and 60 are multiples of 30, so we can apply common factor - 30:

-90-60w = - 30 (3+2w). Then option A is correct.

Now, 90 and 60 are also multiples of 10, so we can apply common factor 10:

-90-60w = 10 (-9-6w). Then option B is correct.

Now, 90 and 60 are also multiples of 3, so we can apply common factor - 3:

-90-60w = - 3 (30+20w). Then option C is incorrect.

Now, 90 and 60 are also multiples of 15, so we can apply common factor 15:

-90-60w = 15 (-6-4w). Then option D is incorrect.

Now, 90 is not a multiple of 20 but we can apply common factor obtainig a decimal number. Applying common factor - 20 we have

-90-60w = - 20 (4.5+3w). Then option E is correct.