Đáp án:

\(\begin{array}{l}
3)x \ne 0\\
4)x \ge  - 3\\
5)\forall x\\
6)2 > x \ge \dfrac{1}{2}\\
7)5 > x \ge 3\\
8)x \ge 1\\
9)\left[ \begin{array}{l}
x \ge \dfrac{3}{2}\\
x <  - 1
\end{array} \right.\\
10)\forall x\\
11)\left[ \begin{array}{l}
x \ge \sqrt 5 \\
x \le  - \sqrt 5 
\end{array} \right.\\
12)x = 1\\
13)x < 1\\
14)\dfrac{{2015}}{{2016}} \ge x\\
15)x >  - 1\\
16)x \ge 0
\end{array}\)

Giải thích các bước giải:

\(\begin{array}{l}
3)DK:x \ne 0\\
4)DK:x + 3 \ge 0\\
 \to x \ge  - 3\\
5)DK:9{x^2} - 6x + 1 \ge 0\\
 \to {\left( {3x - 1} \right)^2} \ge 0\left( {ld} \right)\\
KL:\forall x\\
6)DK:\left[ \begin{array}{l}
\left\{ \begin{array}{l}
2x - 1 \ge 0\\
2 - x > 0
\end{array} \right.\\
\left\{ \begin{array}{l}
2x - 1 \le 0\\
2 - x < 0
\end{array} \right.
\end{array} \right.\\
 \to \left[ \begin{array}{l}
2 > x \ge \dfrac{1}{2}\\
\left\{ \begin{array}{l}
x \le \dfrac{1}{2}\\
x > 2
\end{array} \right.\left( l \right)
\end{array} \right.\\
7)DK:\left\{ \begin{array}{l}
x - 3 \ge 0\\
5 - x > 0
\end{array} \right.\\
 \to 5 > x \ge 3\\
8)DK:\left\{ \begin{array}{l}
x - 1 \ge 0\\
x + 5 \ge 0
\end{array} \right.\\
 \to x \ge 1\\
9)DK:\left[ \begin{array}{l}
\left\{ \begin{array}{l}
2x - 3 \ge 0\\
x + 1 > 0
\end{array} \right.\\
\left\{ \begin{array}{l}
2x - 3 \le 0\\
x + 1 < 0
\end{array} \right.
\end{array} \right.\\
 \to \left[ \begin{array}{l}
x \ge \dfrac{3}{2}\\
x <  - 1
\end{array} \right.\\
10)DK:{x^2} - x + 1 \ge 0\left( {ld} \right)\forall x\\
KL:\forall x\\
11)DK:{x^2} - 5 \ge 0\\
 \to {x^2} \ge 5\\
 \to \left[ \begin{array}{l}
x \ge \sqrt 5 \\
x \le  - \sqrt 5 
\end{array} \right.\\
12)DK: - {x^2} + 2x - 1 \ge 0\\
 \to  - {\left( {x - 1} \right)^2} \ge 0\\
 \to {\left( {x - 1} \right)^2} \le 0\\
 \to x - 1 = 0\\
 \to x = 1\\
13)DK:x - 1 < 0\\
 \to x < 1\\
14)DK:2015 - 2016x \ge 0\\
 \to \dfrac{{2015}}{{2016}} \ge x\\
15)DK:x + 1 > 0\\
 \to x >  - 1\\
16)DK:x \ge 0
\end{array}\)