Question

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)

Answer 1

A : -30(3+2w)

B : (-9-6w) ⋅ 10

E : −20(4.5 + 3w)

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)

Answer 2

A, B and E.

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.