Which of the following inequalities is equivalent to −6 < x < 8? Pick
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, -6 &lt; x &lt; 8, let's say by adding y to this inequality we will get into the above format   -6+y &lt; x+y &lt; 8+y   Now, to move this into the mod format, we need to have (-6+y) + (8+y) = 0 =&gt; y = -1   Thus, -7 &lt; x-1 &lt; 7 =&gt; |x-1| &lt; 7.   Hence, answer is |x - 1| &lt; 7
<result>A</result>
Which of the following inequalities is equivalent to −6 < x < 8?