Question

ok i have a problem and I have no idea what it means.

Use absolute value notation to describe: x is at most 3 units from a.

Answer 1

"x is at most 3 units from a." means x could be 3 units away from 'a' or x could be 2 units away from 'a', etc..


Remember, absolute value is used to determine distance. So for instance, |3|=3 means that the number 3 is 3 units away from 0. Another example is |-6|=6 which tells us that -6 is 6 units away from 0.


In general, |x| represents the distance x is from zero. It can be written as |x-0| since it's really the same thing.


So if we replace the 0 with 'a', then we get |x-a| which represents the distance x is from 'a'


Now because "x is at most 3 units from a.", this means that this distance is capped at 3.


So this means that \[\large |x-a|\le 3\]


So "x is at most 3 units from a." completely translates to the expression \[\large |x-a|\le 3\]