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Distance method works like a charm here, if you can understand what the question is asking then you might not even have to lift your pen.
Eyeballing the points we have to calculate distances from -8, -3, 4 but how?
|x+3| = |x+8| + |x-4|
To understand this, let's visualize these points on the number line and understand what's it asking us,
...........-8........-3..........................4........................
We are asked to calculate a point whose total distance from -8 and 4 is equal to distance from -3.
As we considered the full range, we know there's no solution possible here.
IMO: A
Thanks KarishmaB for throwing light on the distance strategy.
Eyeballing the points we have to calculate distances from -8, -3, 4 but how?
|x+3| = |x+8| + |x-4|
To understand this, let's visualize these points on the number line and understand what's it asking us,
...........-8........-3..........................4........................
We are asked to calculate a point whose total distance from -8 and 4 is equal to distance from -3.
- -8 <= x <= 4 => Now, any point b/w -8 and 4 will have a total distance of 12 (8-(-4)) from both these points, let's pick a number in the middle say 1 then it would be at a distance 9 from -8 and at distance 3 from 4, totaling to 12 and this would be true for any point in the middle. At the same time that point would be at max distance 7 (4-(-3)) from -3 so you cannot get any point x in the middle which can be at a distance 12 from -3.
- x<-8 or x>4 => An interesting observation here is that if you pick any point above 4, it would always be far from -8 than -3 (d(-8) > d(-3)) so the summation of distances from -8 and 4 can never be equal to distance from -3 (d(-8) + d(4) != d(3)) and similarly any point below -8 would be at a greater distance from 4 than -3 (d(4) > d(-3)) making any solution impossible (d(-8) + d(4) != d(3)) .
As we considered the full range, we know there's no solution possible here.
IMO: A
Thanks KarishmaB for throwing light on the distance strategy.
