Which of the following inequalities is equivalent to −8 < x < 6?  Choose the correct choice from the following answers:
A) |x - 1| < 7  B) |x + 2| < 6  C) |x + 3| < 5  D) |x - 2| < 6  E) None of the above
We know that |x| &lt; a means -a &lt; x &lt; a, where Sum of lower limit of x (i.e -a) and the upper limit of x (i.e a), is 0   Given is, -8 &lt; x &lt; 6, let's say by adding y to this inequality we will get into the above format   -8+y &lt; x+y &lt; 6+y   Now, to move this into the mod format, we need to have (-8+y) + (6+y) = 0 =&gt; y = 1   Thus, -7 &lt; x+1 &lt; 7 =&gt; |x+1| &lt; 7.   Hence, answer is None of the above
<result>E</result>
Which of the following inequalities is equivalent to −8 < x < 6?