Đáp án:
$\begin{array}{l}
a)26 - 1.x \le 26x + 26\\
\Rightarrow 26x + x \ge 0\\
\Rightarrow 27x \ge 0\\
\Rightarrow x \ge 0\\
Vậy\,x \ge 0\\
b){x^2} + \left( {26 + 1} \right).x \ge - 26\\
\Rightarrow {x^2} + 26x + x + 26 \ge 0\\
\Rightarrow x\left( {x + 26} \right) + \left( {x + 26} \right) \ge 0\\
\Rightarrow \left( {x + 1} \right)\left( {x + 26} \right) \ge 0\\
\Rightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x + 1 \ge 0\\
x + 26 \ge 0
\end{array} \right.\\
\left\{ \begin{array}{l}
x + 1 \le 0\\
x + 26 \le 0
\end{array} \right.
\end{array} \right. \Rightarrow \left[ \begin{array}{l}
x \ge - 1\\
x \le - 26
\end{array} \right.\\
Vậy\,x \ge - 1;x \le - 26\\
c)\dfrac{{\left( {26 - 1} \right).x}}{{x - 26}} + x < 26x - 26\\
\Rightarrow \dfrac{{25x + x\left( {x - 26} \right)}}{{x - 26}} - 26\left( {x - 1} \right) < 0\\
\Rightarrow \dfrac{{{x^2} - 26x + 25x}}{{x - 26}} - 26\left( {x - 1} \right) < 0\\
\Rightarrow \dfrac{{{x^2} - x}}{{x - 26}} - 26\left( {x - 1} \right) < 0\\
\Rightarrow \left( {x - 1} \right).\left( {\dfrac{x}{{x - 26}} - 26} \right) < 0\\
\Rightarrow \left( {x - 1} \right).\dfrac{{x - 26x + {{26}^2}}}{{x - 26}} < 0\\
\Rightarrow \left( {x - 1} \right).\dfrac{{676 - 25x}}{{x - 26}} < 0\\
\Rightarrow \left( {x - 1} \right)\dfrac{{\left( {25x - 676} \right)}}{{x - 26}} > 0\\
\Rightarrow \left[ \begin{array}{l}
x > 27,04\\
1 < x < 26
\end{array} \right.\\
Vậy\,1 < x < 26\,hoac\,x > 27,04
\end{array}$
