0<4*2^x-4^x inequation

Given the inequality:
$$0 < 4 \cdot 2^{x} - 4^{x}$$
To solve this inequality, we must first solve the corresponding equation:
$$0 = 4 \cdot 2^{x} - 4^{x}$$
Solve:
$$x_{1} = 2$$
$$x_{1} = 2$$
This roots
$$x_{1} = 2$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 2$$
=
$$\frac{19}{10}$$
substitute to the expression
$$0 < 4 \cdot 2^{x} - 4^{x}$$
$$0 < - 4^{\frac{19}{10}} + 4 \cdot 2^{\frac{19}{10}}$$

         4/5      9/10
0 < - 8*2    + 8*2    
    

the solution of our inequality is:
$$x < 2$$

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