# Intersection of two inequation

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.

• This question makes no sense (in English). Please have a native English speaker write the question so it makes sense. Thanks. – David G. Stork Jun 1 '19 at 4:06

## 1 Answer

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

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

• 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! – Eduardo Sebastian Jun 1 '19 at 20:55