IX - 4I ≤ 4
Step-by-step explanation:
The number line indicates that the possible values of x fall within the range:
0 ≤ x ≤ 8
We aim to create an absolute value equation to encompass this set of potential solutions.
An example of such an equation is:
IX - 4I ≤ 4
To form this, we find the midpoint M of our set, which is 4 in this case.
Then, we write:
Ix - MI ≤ IMI
It's important to note my use of the inclusive sign, as the filled dots indicate that the endpoints x = 0 and x = 8 are part of the solution, differing from empty dots which denote an open set requiring < > signs.
Here’s a counterexample: consider
Select the subsets in the following manner:
It's accurate that 
and 
and that 
, but 
The total number of juices equals 27, with the probabilities for each type being as follows: apple juice = 12/27, grape juice = 15/27, sugar-free = 14/27, and not sugar-free = 13/27. Since it has already been established that the chosen juice is not sugar-free, we do not need to factor that probability into our calculations. Of the apple juices, 9 are sugar-free, leaving 3 that are not, and for the grape juices, 5 are sugar-free, resulting in 10 that are not. Consequently, among 13 juices that are not sugar-free, 10 are grape juice, so the likelihood of selecting a non-sugar-free grape juice is 10/13. Therefore, the answer is A). Sorry if my explanation was lengthy; I tend to elaborate.
