alex.gellatly wrote:For this question I am going too use the ~ symbol for absolute value as I don't know to type absolute value, sorry
Is |x| + |x-1| = 1?
1 x is greater than or equal to 0
2. x is less than or equal to 1
I put E, but the oa is c, can someone explain.
Thanks
The easiest approach is to plug in values.
If 0≤x≤1 -- the result of combining the two statements -- the answer to the question stem is always YES:
|0| + |0-1| = 1.
|.5| + |.5-1| = 1.
|1| + |1-1| = 1.
Since the answer is always YES, the two statements combined are SUFFICIENT.
The correct answer is
C.
Number line approach:
|x-y| = the distance between x and y.
Thus, in the problem at hand:
|x| = the distance between x and 0.
|x-1| = the distance between x and 1.
Draw a number line so that x is between 0 and 1:
<-----0-------x------1-------------->
..................|x|.......|x-1|...............................
We can see that the sum of the two distances is 1.
In other words:
If 0≤x≤1, then |x| + |x-1| = 1.
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