Question

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

Answer 1

[x-] ??

Answer 2

sorry it is -5

Answer 3

and what is [] <--- is it floor or ceil??

Answer 4

or absolute value??

Answer 5

absolute value

Answer 6

you ment this right/?

\[|x−5|+|x−1|<2\]

Answer 7

no solution
http://www.wolframalpha.com/input/?i= |x-5|+%2B|x-1|++-+2

Answer 8

yes u r correct 0 solution

Answer 9

but how?

Answer 10

is
|x-5| + |x-1| ever less than zero??

Answer 11

sorry .. ever less than 2??
or |x-5| + |x-1| - 2 less than zero ... check the graph

Answer 12

so...... the sign should be > to have solution is it...

Answer 13

No ... you just need to find a point for which the above in equality is true
eg
3 < x < 4

3.5 is greater than 3 and less than 4 ... so this is true ... so this is solution

Answer 14

can u explain it more..... plzzzz

Answer 15

You just need to find the numbers that satisfy the given condition.

Answer 16

i mean you have to find that numbers for which the given condition is true.

for eg: 1 > x > 2 (find a number that is less than and greater than two ... find it's solution

Answer 17

plzzz help !

Answer 18

i did nt understand

Answer 19

plzz help any one plz!!

Answer 20

See the attached graph to see that |x-5| + | x-1| is always bigger than 2.
There are no solutions.
If this does not convince you try to consider three cases
x <1
1< x < 5
x > 5
In each case try to solve it. I will do the first case for you
if x< 1
the inequality becomes
5-x + 1 -x < 2
-2 x < -4
x > 2 contradiction with the face that x<1
Mimic for the remaining cases and conclude.

Answer 21

@eliassaab the next i got x<4

Answer 22

1 < x < 5
|x-5| + | x-1| < 2
5- x + x -1 < 2
4 < 2
contradiction.
Do the last case.

Answer 23

i f x > 5
|x-5| + | x-1| < 2
x-5 + x -1 < 2
2 x < 8
x < 4
but x > 5
contradiction.

Answer 24

so......

Answer 25

Did you understand it?

Answer 26

yes

Answer 27

then ................

Answer 28

You are done. You showed that all cases lead to contradictions. So there are no solutions. Did you get it now?

Answer 29

ok

Answer 30

yw