Question

The number of solutions that are possible for the in equality \[\left[ x-5 \right] + \left[ x -1\right]<2\] is?

Answer 1

if this is absolute value, no solutions

Answer 2

yes u r correct the answer is 0 can u show this plzz

Answer 3

seems like the minimum number of |x-5| + |x-1| = 4
thus there are 0 solutions where its less than 2

Answer 4

have to work in cases.
if \(x>5\) then \(|x-5|=x-5\) and \(|x-1|+x-1\) solve ...
ok dumbcow answer much better so i shut up

Answer 5

haha

Answer 6

i did nt understand dude.....

Answer 7

and while it is true, i am not sure how you see that right away. there is still a computation to do right?

Answer 8

yes i think we have to take four cases.....

Answer 9

if \(1<x<5\) then you have \(|x-5|+|x-1|=-x+5+x-1=4\) a constant

Answer 10

no i agree as well, we should look at each case to show it
i just analyzed the graphs and noticed from 1 to 5 that sum was always 4

Answer 11

if \(x>5\) you have \(x-5+x-1=2x-6\) and \(2x-6>4\) if \(x>5\)

Answer 12

so i guess it does come down to cases after all
i will let you do the last case \(x<1\) for yourself, but you will find that the expression is greater than 4 in that case too

Answer 13

x-5-x+1<2

Answer 14

-4<2..........

Answer 15

plzz help>..........

Answer 16

if \(x<1\) then both \(|x-5|=-x+5\) and \(|x-1|=-x+1\) and so
\[|x-5|+|x-1|=-x+5-x+1=-2x+6\]

Answer 17

and since \(x<1\) we know \(-2x+6>4\) and if it is greater than 4, it is certainly not less than two

Answer 18

x>1

Answer 19

plzz help plzz......

Answer 20

i am stuck middle way.....

Answer 21

@Ishaan94 @blues @Aadarsh @myininaya @Mertsj
plzz help

Answer 22

@imranmeah91 hel-pp