SOLUTION: If |x-5|<4, which of the following is a possible value of X?

Question 1040325: If |x-5|<4, which of the following is a possible value of X?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Rule: if |x| < k then -k < x < k where k is some positive number.

For instance, if |x| < 5 then -5 < x < 5

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Use that rule to go from |x-5| < 4 to -4 < x-5 < 4

Now let's add 5 to all sides of -4 < x-5 < 4 to get

-4 < x-5 < 4
-4+5 < x-5+5 < 4+5
1 < x + 0 < 9
1 < x < 9

So you can pick any number between 1 and 9 for x. You cannot pick 1. You cannot pick 9.
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