Which of the following inequalities is equivalent to −4 < x < 8?
Choose one.
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, -4 &lt; x &lt; 8, let's say by adding y to this inequality we will get into the above format   -4+y &lt; x+y &lt; 8+y   Now, to move this into the mod format, we need to have (-4+y) + (8+y) = 0 =&gt; y = -2   Thus, -6&lt; x-2 &lt; 6 =&gt; |x-2| &lt; 6.   Hence, answer is |x - 2| &lt; 6
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Which of the following inequalities is equivalent to −4 < x < 8?