Question

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

Answer 1

the answer is 0 plzz can anyone solve for it

Answer 2

For x < 1 the inequality becomes
\[
- x + 5 - x +1 <2\\
-2x < -3\\
x> \frac 3 2
\]
Contradiction

Answer 3

Do the same reasoning for 1< x < 5 and for x>5