Problem about inequation with absolute value I have this statement:

It can be assured that | p | ≤ 2.4, if it is known that:
(1) -2.7 ≤ p <2.3
(2) -2.2 < p ≤ 2.6

My development was:
First, $ -2.4 \leq p \leq 2.4$
With $1)$ by itself, that can't be insured, same argument for $2)$
Now, i will use $1)$ and $2)$ together, and the intersection between this intervals are: $(-2.2, 2.3)$. So, this also does not allow me to ensure that | p | ≤ 2.4, since, there are some numbers that are outside the intersection of these two intervals, for example 2.35 is outside this interval. 
But according to the guide, the correct answer must be $1), 2)$ together. And i don't know why.
Thanks in advance.
 A: You getting confused by a strong premise implying a weak conclusion. 
1 and 2 together say precisely:  $p\in (-2.2,2.3) $
And you are asking to conclude $p\in [-2.4,2.4] $.
That's simply a matter of noting if $(-2.2, 2.3) \subset [-2.4,2.4] $.  And if $p $ is in a smaller subset, then we can conclude $p $ must therefore also be in the bigger superset.
Or in other words:
$-2.2 < p < 2.3\implies $
$-2.4\le -2.2 < p <2.3 \le 2.4\implies $
$-2.4\le p \le 2.4$
....
An analogy:
We can conclude $p $ is a somewhat green article of clothing if we know both 
1: $p$ is a hat.
2: $p$ is precisely the color an emerald takes when viewed at noon on the summer solstice on the equator.
In your question,  1 tells you that $p <2.3$ so you can conclude $p\le 2.4$.  ($p $ is a hat so you can conclude $p $ is an article of clothing.)
And 2 tells you that $-2.2 <p $ so you can conclude $-2.4\le p $.  ($p $ is the color of emeralds so you can conclude $p $ is green.)
Together 1 and 2 tell you $-2.2<p <2.3$ so you can conclude $-2.4\le p\le 2.4$.  (Together you know $p $ is a hat the color of emeralds in a certain condition so you can conclude $p $ is a green article of clothing.)
Strong premise.  Weak result.
A: $ -2.4 \leq p \leq 2.4$
$ -2.7 \leq p < 2.3$
$-2.2 < p \leq 2.6 $
Your answer is common intersection of these inequalities. 
$ p \in (-2.2, 2.3)$
A: The point is that if you use $1$ and $2$ together you know $-2.2 \lt p \lt 2.3$.  This does allow you to ensure $|p| \le 2.4$ because all numbers in the interval are less than $2.4$ in absolute value.  The fact that there are numbers outside the interval that also qualify does not matter at all.  If I told you that $0.1 \le p \le 0.9$ you could assure me that $|p| \le 2.4$.  You could also make a stronger statement, like $|p| \le 1$ or $|p| \le 0.9$, but that doesn't mean the one with $2.4$ is incorrect.
