Question 1190443
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a = Ashley's estimate
b = true amount
a-b = difference of the two items


The difference represents how far off Ashley is. 
For example, if she guesses a= 10 marbles but there's actually b = 7 marbles, then she would be a-b = 10-7 = 3 marbles off.


For cases when b is larger than a, like a = 7 and b = 10, we have
a-b = 7-10 = -3
We can't have a negative distance. We want to be able to express this gap as some positive number or zero.


This is where absolute value comes in.
|a-b| ensures that the difference is never negative.
The lowest it can go is 0. 
It represents the distance from a to b on the number line.


To be within 15 marbles means that the distance |a-b| is 15 or smaller
Put another way: the worst Ashley could guess is that she's 15 too high or 15 too low compared to the actual count.


This leads us to {{{abs(a-b) <= 15}}}


That directly points to {{{-15 <= a-b <= 15}}} based on the rule that 
{{{abs(x) <= k}}} is equivalent to {{{-k <= x <= k}}} for any positive number k.



Answer: Choice A  {{{-15 <= a-b <= 15}}}
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