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I have this statement:

All numbers that are more than 10 units of 6 and less than 16 units out of 8 are represented by:

My development was:

First, $n > 16$ that is "more than 10 units of 6"

Second, $n < 24$ that is "less than 16 units of 8"

And the intersection between the two interval are $(16,24)$.

But according to the guide, the correct answer must be $ ]-8, -4[ \cup ]16,24[$, and i don't know why. Thanks in advance.

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    $\begingroup$ This question makes no sense (in English). Please have a native English speaker write the question so it makes sense. Thanks. $\endgroup$ – David G. Stork Jun 1 '19 at 4:06
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I believe the question should be interpreted as follows. The first set (that I will call $A$) is the set of numbers whose distance to $6$ is more than $10$, i.e. $$A = \{x\ :\ |x-6|>10\} = ]-\infty, -4[\ \cup\ ]16, \infty[.$$ The second set $B$ is the set of numbers, whose distance to $8$ is less than $16$, so

$$B = \{x\ :\ |x-8|<16\} = ]-8,24[.$$

The answer to the question is the intersection $A\cap B$, which is

$$A\cap B = ]-8,-4[\ \cup\ ]16, 24[.$$

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    $\begingroup$ My mistake was to think only of positive numbers. However, -5, is also more than 10 units out of 6. Same argument for 8 .. Thank you! $\endgroup$ – Eduardo Sebastian Jun 1 '19 at 20:55

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