6^x-7^x>0 inequation

Given the inequality:
$$6^{x} - 7^{x} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$6^{x} - 7^{x} = 0$$
Solve:
$$x_{1} = 0$$
$$x_{1} = 0$$
This roots
$$x_{1} = 0$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10}$$
=
$$- \frac{1}{10}$$
substitute to the expression
$$6^{x} - 7^{x} > 0$$
$$- \frac{1}{\sqrt[10]{7}} + \frac{1}{\sqrt[10]{6}} > 0$$

   9/10    9/10    
  7       6        
- ----- + ----- > 0
    7       6      
    

the solution of our inequality is:
$$x < 0$$

 _____          
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       x1