Solve for x?

Question

xln(x) + 1 > x + ln(x)

e^1/x > 1

Any help would be appreciated. THANK YOU!

Answer 1

(2) e^(1/x) > 1

When e^(1/x) = 1, (taking natural logs of both sides)
(1/x) = 0
x = infinity

Any positive number x that is less than infinity satisfies the inequality.

(1) The solution to
xln(x) + 1 = x + ln(x)
is x = 1. Values x between 0 and satisfy the inequality.