Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
1,\\
{x^2} > 4\\
\Leftrightarrow {x^2} > {2^2}\\
\Leftrightarrow \left| x \right| > 2\\
\Leftrightarrow \left[ \begin{array}{l}
x > 2\\
x < - 2
\end{array} \right.\\
2,\\
{x^2} < 9\\
\Leftrightarrow {x^2} < {3^2}\\
\Leftrightarrow \left| x \right| < 3\\
\Leftrightarrow - 3 < x < 3\\
3,\\
{x^2} \ge 25\\
\Leftrightarrow {x^2} \ge {5^2}\\
\Leftrightarrow \left| x \right| \ge 5\\
\Leftrightarrow \left[ \begin{array}{l}
x \ge 5\\
x \le - 5
\end{array} \right.\\
4,\\
{x^2} \ge 16\\
\Leftrightarrow {x^2} \ge {4^2}\\
\Leftrightarrow \left| x \right| \ge 4\\
\Leftrightarrow \left[ \begin{array}{l}
x \ge 4\\
x \le - 4
\end{array} \right.\\
5,\\
{\left( {x - 1} \right)^2} \ge 4\\
\Leftrightarrow {\left( {x - 1} \right)^2} \ge {2^2}\\
\Leftrightarrow \left| {x - 1} \right| \ge 2\\
\Leftrightarrow \left[ \begin{array}{l}
x - 1 \ge 2\\
x - 1 \le - 2
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x \ge 3\\
x \le - 1
\end{array} \right.\\
6,\\
{\left( {1 - 2x} \right)^2} \le 0,09\\
\Leftrightarrow {\left( {1 - 2x} \right)^2} \le \frac{9}{{100}}\\
\Leftrightarrow {\left( {1 - 2x} \right)^2} \le {\left( {\frac{3}{{10}}} \right)^2}\\
\Leftrightarrow - \frac{3}{{10}} \le 1 - 2x \le \frac{3}{{10}}\\
\Leftrightarrow - \frac{3}{{10}} \le 2x - 1 \le \frac{3}{{10}}\\
\Leftrightarrow - \frac{3}{{10}} + 1 \le 2x \le \frac{3}{{10}} + 1\\
\Leftrightarrow \frac{7}{{10}} \le 2x \le \frac{{13}}{{10}}\\
\Leftrightarrow \frac{7}{{20}} \le x \le \frac{{13}}{{20}}
\end{array}\)
