<PRE><B>Question 1199343</B>
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Add four to all sides of the 1st inequality
-3 &lt; x &lt; 0
-3+4 &lt; x+4 &lt; 0+4
1 &lt; x+4 &lt; 4
The inequality signs stay the same for now.


Then apply the reciprocal to all three sides. 
This flips the direction of the inequality signs.
It&#39;s like saying how 2 &gt; 1/3 flips to 1/2 &lt; 3.


So,
1 &lt; x+4 &lt; 4
1/1 &gt; 1/(x+4) &gt; 1/4
1 &gt; 1/(x+4) &gt; 1/4


Now let&#39;s go from the form p &gt; q &gt; r to r &lt; q &lt; p
1 &gt; 1/(x+4) &gt; 1/4
1/4 &lt; 1/(x+4) &lt; 1
In other words, swap the 1st and last sides so that the &quot;greater than&quot; signs become &quot;less than&quot; signs.


Compare that to the form
a &lt; 1/(x+4) &lt; b
to find that
a = &lt;font color=red&gt;1/4&lt;/font&gt;
b = &lt;font color=red&gt;1&lt;/font&gt;
which are the final answers.
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