To solve this inequality, we need to use the properties of logarithms.

First, we can simplify the given inequality:

lgx + 2lg2 < 0.5lg49 - lg5

Since lg2 = 1, we can simplify further:

lgx + 2 < 0.5(2) - 1

lgx + 2 < 1 - 1

lgx + 2 < 0

Subtracting 2 from both sides:

lgx < -2

Now we can rewrite this inequality in exponential form:

x < 10^(-2)

So the solution to the inequality is x < 0.01.