xx+1<10-5 hold if
-105<x+1<10-4
-100001-1<x<99999-1
110000<x<1
99999-1<x<100001-1
Explanation for the correct option
Solve the inequality:
Formula:
Absolute value formula: if a≤b then, -b≤a≤b
The given inequality is,
xx+1<10-5
⇒ x+1-1x+1<10-5
⇒ 1-1x+1<10-5
⇒ -10-5<1-1x+1<10-5 Byabsolutevalueformula
⇒ -1-10-5<-1x+1<-1+10-5 Subtracted1fromeachterm
⇒ 1-10-5<1x+1<1+10-5 Multipliedeachtermby-1
⇒ 1-1100000<1x+1<1+1100000
⇒ 99999100000<1x+1<100001100000
⇒ 100000100001<x+1<10000099999 Takeresiprocal
⇒ 100000100001-1<x+1-1<10000099999-1 Subtracted1fromeachterm
⇒ -1100001<x<199999
⇒ -100001-1<x<99999-1
Hence, the correct option is B)-100001-1<x<99999-1.