If y = |x+3| + |4-x|, does y=7?
1. x < 4
2. x > -3
|a-b| = the DISTANCE between a and b.
|a+b| = |a-(-b)| = the DISTANCE between a and -b.
Thus:
|x+3| = the distance between x and -3.
|4-x| = the distance between 4 and x.
y = the SUM of these two distances.
Question stem rephrased:
Is the sum of the two distances equal to 7?
The distance between -3 and 4 is 7.
Thus, if x is BETWEEN these two endpoints, then the sum of the two distances will be EQUAL TO 7:
-3 <--- |x+3| ---> x <---|4-x|---> 4.
Here, |x+3| + |4-x| = the distance between -3 and 4 = 7.
By extension, if x is BEYOND either endpoint -- if x is to the left of -3 or to the right of 4 -- then the sum of the two distances will be GREATER THAN 7.
Statement 1: x < 4
If x=2, then x is between -3 and 4.
If x=-10, then x is to the left of -3.
INSUFFICIENT.
Statement 2: x > -3
If x=2, then x is between -3 and 4.
If x=10, then x is to the right of 4.
INSUFFICIENT.
Statements combined:
-3 < x < 4.
SUFFICIENT.
The correct answer is
C.
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