Đáp án:

\(\begin{array}{l}
a)x \ge  - \dfrac{3}{4}\\
e)\left[ \begin{array}{l}
x \ge \sqrt 3 \\
x \le  - \sqrt 3 
\end{array} \right.\\
i)\left[ \begin{array}{l}
x \ge 3\\
x \le  - 1
\end{array} \right.\\
b)x \ge \dfrac{3}{2}\\
f)\forall x\\
k)3 > x \ge  - 2\\
c) - 3 \ge x\\
g)2 \ge x \ge  - 2\\
m)\left\{ \begin{array}{l}
x \ge 1\\
x \ne 5
\end{array} \right.
\end{array}\)

Giải thích các bước giải:

\(\begin{array}{l}
a)DK:4x + 3 \ge 0 \to x \ge  - \dfrac{3}{4}\\
e)DK:{x^2} - 3 \ge 0 \to {x^2} \ge 3 \to \left[ \begin{array}{l}
x \ge \sqrt 3 \\
x \le  - \sqrt 3 
\end{array} \right.\\
i)DK:{x^2} - 2x - 3 \ge 0 \to \left( {x - 3} \right)\left( {x + 1} \right) \ge 0\\
 \to \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x - 3 \ge 0\\
x + 1 \ge 0
\end{array} \right.\\
\left\{ \begin{array}{l}
x - 3 \le 0\\
x + 1 \le 0
\end{array} \right.
\end{array} \right. \to \left[ \begin{array}{l}
x \ge 3\\
x \le  - 1
\end{array} \right.\\
b)DK:2x - 3 \ge 0 \to x \ge \dfrac{3}{2}\\
f)DK:{x^2} - 2x + 5 \ge 0 \to {x^2} - 2x + 1 + 4 \ge 0\\
 \to {\left( {x - 1} \right)^2} + 4 \ge 0\left( {ld} \right)\forall x\\
KL:\forall x\\
k)DK:\left[ \begin{array}{l}
\left\{ \begin{array}{l}
x + 2 \ge 0\\
3 - x > 0
\end{array} \right.\\
\left\{ \begin{array}{l}
x + 2 \le 0\\
3 - x < 0
\end{array} \right.
\end{array} \right. \to \left[ \begin{array}{l}
3 > x \ge  - 2\\
\left\{ \begin{array}{l}
x \le  - 2\\
3 < x
\end{array} \right.\left( l \right)
\end{array} \right.\\
 \to 3 > x \ge  - 2\\
c)DK: - x - 3 \ge 0 \to  - 3 \ge x\\
g)DK:4 - {x^2} \ge 0 \to 4 \ge {x^2}\\
 \to 2 \ge x \ge  - 2\\
m)DK:\left\{ \begin{array}{l}
x - 1 \ge 0\\
\sqrt {x - 1}  \ne 2
\end{array} \right. \to \left\{ \begin{array}{l}
x \ge 1\\
x - 1 \ne 4
\end{array} \right.\\
 \to \left\{ \begin{array}{l}
x \ge 1\\
x \ne 5
\end{array} \right.
\end{array}\)