Question

How do you solve `|k-2|>=3`?

Answer 1

`kin[-1,-oo) larr` all the value from -1 to negative infinity

`kin[5,+oo) larr` all the value from +5 to positive infinity

`"that is: "5<=k<=-1`

Explanation:

Absolute value is counting how far away from 0 the number is. This is considered in both the positive and negative directions.

Some value between two vertical lines written as `|"some value"|` is always considered as `+"some value"` when thinking about the solution.

So we have `" some value" = |+-" some value"|`

This means that what is inside the two vertical lines can be either of positive or negative.

Thus we have the two condition `|k-2|>=|+-3|`
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Set

`k-2>= +3 =>color(red)( k>=5) ->` further away from 0 in the positive direction.

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Set

`k-2<=-3 =>color(red)(k<=-1)->` further away from 0 in the negative direction.
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