Answer:
a)
i) we have the equation:
3*x - 2*y
We want to find a common multiple of 3 and 2.
One can be:
3*6 = 18
2*9 = 18
And both numbers 6 and 9 are on the list, then if we take:
x = 6, y = 9
we get:
3*6 - 2*9 = 18 - 18 = 0
The solution is x = 6, y = 9.
ii) The greatest possible value of:
3*x - 2*y
Will be when x is the largest value of the list (because it is on the positive term) and y is the smallest value on the list (because it is on the negative term)
then we need to have x = 10, y = 5
The value will be:
3*10 - 2*5 = 30 - 10 = 20
iii) Now we want to have the smallest value on x, and the largest one on y, then:
x = 5, y = 10
The smallest value of the equation will be:
3*5 - 2*10 = 15 - 20 = -5
B) We want to solve:
5*(a - 4*b)
when:
a = -7
b = 1/4
This is kinda easy, we just need to replace the variables in the equation to get:
5*(a - 4*b) = 5*(-7 - 4*(1/4)) = 5*(-7 - 4/4) = 5*-8 = -40
