prata wrote:What is the value of |x + 5| + |x - 3|?
1. x^2 < 25
2. x^2 > 9
What is the value of |x + 5| + |x - 3|?
The critical points are the values that make the absolute values equal to 0.
Here, the critical points are -5 and 3.
The distance between the critical points is the LEAST POSSIBLE VALUE for the expression in blue.
The distance between -5 and 3 is 8.
Thus, the least possible value for the expression in blue is 8.
If x is between the critical points of -5 and 3, inclusive, then the expression in blue will be equal to the LEAST POSSIBLE VALUE (8):
If x=0, then |x + 5| + |x - 3| = |0+5| + |0-3| = 8.
If x=-2, then |x + 5| + |x - 3| = |-2+5| + |-2-3| = 8.
If x=3, then |x + 5| + |x - 3| = |3+5| + |3-3| = 8.
If x is NOT between the critical points of -5 and 3, inclusive, then the expression in blue will be equal to a VALUE GREATER THAN 8:
If x=4, then |x + 5| + |x - 3| = |4+5| + |4-3| = 10.
If x=10, then |x + 5| + |x - 3| = |10+5| + |10-3| = 22.
If x=-7, then |x + 5| + |x - 3| = |-7+5| + |-7-3| = 12.
Both statements are satisfied by x=-4.
In this case, x is between -5 and 3, inclusive, so the expression in blue will be equal to the least possible value (8).
Both statements are satisfied by x=4.
In this case, x is NOT between -5 and 3, inclusive, so expression in blue will equal to a value greater than 8.
Since the expression in blue can be different values, the two statements combined are INSUFFICIENT.
The correct answer is
E.
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