\[\sqrt{a + 2} + \sqrt{2a + 1}\]
\[\left\{ \begin{matrix} a + 2 \geq 0\ \ \ \\ 2a + 1 \geq 0 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\left\{ \begin{matrix} a \geq - 2\ \ \ \\ 2a \geq - 1 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} a \geq - 2\ \ \ \\ a \geq - 0,5 \\ \end{matrix} \right.\ \]
\[Выражение\ имеет\ смысл\ при\ a \geq - 0,5.\]
\[1)\ Имеет\ смысл\ при\ a = 0;\ \ 3;10.\]
\[2)\ Не\ имеет\ смысла\ при\ a = - 1;\ - 2;\ - 5.\]
\[\frac{5}{9} = \frac{5000}{9000}\]
\[\frac{551}{1000} = \frac{4959}{9000}\]
\[\frac{5000}{9000} > \frac{4959}{9000}\]
\[\frac{5}{9} > 0,551.\]
\[\frac{1}{8} < x < \frac{1}{7}\]
\[\frac{1}{8} = 0,125;\ \ \frac{1}{7} = 0,(142857)\]
\[x = 0,1325.\]
\[Ответ:0,1325.\]
\[- 103
otin N\]
\[\sqrt{0,16} \in Q\]
\[- \frac{5}{16} \in R\]
\[0,5a \geq 0,5b\]
\[a \geq b\]
\[Верные\ равенства:\]
\[a + 5 \geq b + 5\]
\[\frac{1}{3}a + 1 \geq \frac{1}{3}b + 1.\]
\[Неверные\ равенства:\]
\[a \leq b.\]
\[7 - 2x \geq 21\]
\[- 2x \geq 21 - 7\]
\[- 2x \geq 14\]
\[x \leq - 7.\]
\[x - 4 \cdot (x - 3) < 3 - 6x\]
\[x - 4x + 12 + 6x < 3\]
\[3x < 3 - 12\]
\[3x < - 9\]
\[x < - 3.\]
\[\left\{ \begin{matrix} 4x - 5 < 1\ \ \ \ \ \ \ \ \\ x + 4 < 3x + 2 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\left\{ \begin{matrix} 4x < 5 + 1\ \ \ \ \ \ \ \ \\ x - 3x < 2 - 4 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} 4x < 6\ \ \ \ \ \ \\ - 2x < - 2 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\left\{ \begin{matrix} x < 1,5 \\ x > 1\ \ \ \\ \end{matrix} \right.\ \]
\[Ответ:x \in (1;1,5).\]
\[m = (5 \pm 0,03)\ кг.\]
\[4,97\ кг \leq m \leq 5,003\]
\[Масса\ 4,9\ кг\ не\ удовлетворяет\ условию.\]
\[Ответ:нет.\]
\[\frac{16 - 3x}{3} + \frac{3x + 7}{4} < 0\]
\[4 \cdot (16 - 3x) + 3 \cdot (3x + 7) < 0\]
\[64 - 12x + 9x + 21 < 0\]
\[- 3x < - 85\]
\[x > \frac{85}{3}\]
\[x > 28\frac{1}{3}.\]
\[x_{наим} = 29.\]
\[Ответ:29.\]
\[S = a^{2};\ \ a = \sqrt{5}.\]
\[2,2 < \sqrt{5} < 2,3\]
\[{2,2}^{2} < S < {2,3}^{2}\]
\[4,84 < S < 5,29.\]
\[\sqrt{37} + \sqrt{35} < 12\]
\[\left( \sqrt{37} + \sqrt{35} \right)^{2} < 12^{2}\]
\[37 + 2 \cdot \sqrt{37} \cdot \sqrt{35} + 35 < 144\]
\[2 \cdot \sqrt{37} \cdot \sqrt{35} < 144 - 72\]
\[2 \cdot \sqrt{37} \cdot \sqrt{35} < 72\]
\[\sqrt{37} \cdot \sqrt{35} < 36\]
\[\left( \sqrt{37 \cdot 35} \right)^{2} < 36^{2}\]
\[37 \cdot 35 < 1295\]
\[1295 < 1296\]
\[Что\ и\ требовалось\ доказать.\]