The median of a set of three numbers is x. there at least three numbers in the set. write an algebraic expression, in terms of x, to represent the median of the new set of numbers obtained by a. adding 1/8 to every number in the set b. subtracting 9 1/4 from every number in the set c. multiplying -5.8 to every number in the set and then adding 3 to the resulting numbers d. dividing every number in the set by 0.5 and then subtracting 1 from the resulting numbers e. adding 7.2 to the greatest number in the set f. subtracting 4.2 from the least number in the set

The median of a set of three numbers is x. there at least three numbers in the set. Write an algebraic expression, in terms of x, to represent the median of the new set of numbers obtained by
a] adding 1/8 to every number in the set
Let the numbers be w,x,y
adding 1/8 to the number we get:
(w+1/8),(x+1/8),(y+1/8)
the new median will be:
(x+1/8)

b. subtracting 9 1/4 from every number in the set
Given our data set is w,x,y
adding 9 1/4 to each number we get:
(w+9 1/4),(x+9 1/4), (y+9 1/4)
thus the new median is:
(x+9 1/4)

c]multiplying -5.8 to every number in the set and then adding 3 to the resulting numbers
Multiplying each number by -5.8 we get:
(-5.8w),(-5.8x),(-5.8y)
adding 3 to these numbers we get:
(-5.8w+3),(-5.8x+3),(-5.8y+3)
thus the new median is:
(-5.8x+3)

d]dividing every number in the set by 0.5 and then subtracting 1 from the resulting numbers
dividing each number in our set by 0.5 we get:
(w/0.5),(x/0.5),(y/0.5)
this will give us:
(2w),(2x),(2y)
then subtracting 1 from the above we get:
(2w-1),(2x-1),(2y-1)
thus the median will be:
(2x-1)

e. adding 7.2 to the greatest number in the set
from our set:
w.x.y
the greatest number is y, then adding 7.2 to the greatest numbers gives us:
y+7.2
thus new series is:
w,x,y+7.2
thus the median is:
x
Conclusion
The median doesn't change

f. subtracting 4.2 from the least number in the set
from our set w,x,y; subtracting 4.2 from the least number gives us:
w-4.2
the new set is:
w-4.2, x, y
thus the new median is x
Conclusion
The median doesn't change

Distributive property

Um what? rephrase that ?