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18 Mar 2025, 11:53
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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.
24 Mar 2026, 21:13
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|x+3| – |4-x| = |8+x| How many solutions will this equation have?
-8, -3, 4
Case 1: x<=-8
-x-3 + x-4 = -8-x
x=-1
No solution since x=-1 does not lie in x<=-8
Case 2: -8<x<=-3
-x-3 + x-4 = x+8
x = -15
No solution since x=-15 does not lie in -8<x<=-3
Case 3: -3<x<=4
x+3 + x-4 = x+8
x = 9
No solution since x=9 does not lie in -3<x<=4
Case 4: x>4
x+3+4-x=x+8
x = -1
No solution since x=-1 does not lie in x>4
IMO A
-8, -3, 4
Case 1: x<=-8
-x-3 + x-4 = -8-x
x=-1
No solution since x=-1 does not lie in x<=-8
Case 2: -8<x<=-3
-x-3 + x-4 = x+8
x = -15
No solution since x=-15 does not lie in -8<x<=-3
Case 3: -3<x<=4
x+3 + x-4 = x+8
x = 9
No solution since x=9 does not lie in -3<x<=4
Case 4: x>4
x+3+4-x=x+8
x = -1
No solution since x=-1 does not lie in x>4
IMO A
