[tex]7*(\frac{2}{14})^{x+1} \leq 1[/tex]

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вопрос

To solve this inequality, we can start by simplifying the expression:

[tex]7(\frac{2}{14})^{x+1} = 7(\frac{1}{7})^{x+1} = 7(\frac{1}{7})^{x}(\frac{1}{7})[/tex]

[tex]= (\frac{7}{7})^{x}*(\frac{1}{7}) = (\frac{1}{7})^{x}[/tex]

So, our inequality becomes:

tex^{x} \leq 1[/tex]

Since [tex]\frac{1}{7}[/tex] is a proper fraction (less than 1), raising it to any power x will result in a decreasing value. Therefore, for tex^{x}[/tex] to be less than or equal to 1, x must be a non-negative value.

Therefore, the solution to the inequality is [tex]x \geq 0[/tex].