Mo2men wrote:If |x| < 20 and |x - 8| > |x + 4|, which of the following expresses the allowable range for x?
(A) -12 < x < 12
(B) -20 < x < 2
(C) -20 < x < -12 and 12 < x < 20
(D) -20 < x < -8 and 4 < x < 20
(E) -20 < x < -4 and 8 < x < 20
Source: Magoosh
Alternate approach 2:
|a-b| = the distance between a and b.
|a+b| = |a-(-b)| = the distance between a and -b.
|x - 8| > |x + 4|.
In words:
The distance between x and 8 is greater than the distance between x and -4.
In other words, x is CLOSER TO -4 THAN TO 8.
Plotted on a number line:
<----- (-4) ---- 2 ---- 8 ----->
Since 2 is halfway between -4 and 8, the blue portion is composed of all values closer to -4 than to 8.
The blue portion indicates that x<2.
|x|<20 constrains x to values between -20 and 20.
Thus:
-20 < x < 2.
The correct answer is
B.
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