\[\sqrt{a + 3} + \sqrt{2a + 4}\]
\[\left\{ \begin{matrix} a + 3 \geq 0\ \ \\ 2a + 4 \geq 0 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\left\{ \begin{matrix} a \geq - 3\ \ \\ 2a \geq - 4 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} a \geq - 3 \\ a \geq - 2 \\ \end{matrix} \right.\ \]
\[Выражение\ имеет\ смысл\ при\ a \geq - 2.\]
\[Имеет\ смысл:\]
\[a = - 2;\ 0;2.\]
\[Не\ имеет\ смысла:\]
\[a = - 3;\ - 5;\ - 10.\]
\[\frac{5}{6} = \frac{2500}{3000};\ \ \ 0,834 = \frac{834}{1000} = \frac{2502}{3000}.\]
\[\frac{2500}{300} < \frac{2502}{3000}\]
\[\frac{5}{6} < 0,834.\]
\[\frac{1}{4} = 0,25;\ \ \frac{1}{3} = 0,(3):\]
\[x = 0,2678.\]
\[Ответ:0,2678.\]
\[- \pi \in R\]
\[15 \in N\]
\[\frac{3}{7}
otin Z\]
\[\frac{2}{3}a \leq \frac{2}{3}b\]
\[a \leq b.\]
\[Верные\ неравенства:\]
\[a \leq b\]
\[2 - a \geq 2 - b.\]
\[Неверные\ неравенства:\]
\[7a \geq 7b.\]
\[1 - 3x > 16\]
\[- 3x > 15\]
\[x < - 5.\]
\[3 - 2 \cdot (x - 8) \leq 1 - 5x\]
\[3 - 2x + 16 + 5x \leq 1\]
\[3x \leq 1 - 19\]
\[3x \leq - 18\]
\[x \leq - 6.\]
\[\left\{ \begin{matrix} 10x - 1 \geq 2\ \ \ \ \ \ \\ 4 - x \geq 2x + 1 \\ \end{matrix}\ \right.\ \text{\ \ \ \ \ }\left\{ \begin{matrix} 10x \geq 3\ \ \ \ \\ - 3x \geq - 3 \\ \end{matrix} \right.\ \text{\ \ \ \ }\left\{ \begin{matrix} x \geq 0,3 \\ x \leq 1\ \ \ \\ \end{matrix} \right.\ \]
\[Ответ:x \in \lbrack 0,3;1\rbrack.\]
\[m = (3 \pm 0,03)\ кг.\]
\[2,97\ кг \leq m \leq 3,03\ кг.\]
\[Масса\ 3,01\ кг\ удовлетворяет\ условию.\]
\[Ответ:да.\]
\[\frac{1 + x}{2} > \frac{5x - 3}{5}\]
\[5 \cdot (1 + x) > 2 \cdot (5x - 3)\]
\[5 + 5x > 10x - 6\]
\[5x < 11\]
\[x < 2,2.\]
\[x_{наиб} = 2.\]
\[Ответ:2.\]
\[S = a^{2};\ \ a = \sqrt{3}\ см.\]
\[1,7 < \sqrt{3} < 1,8\ \]
\[{1,7}^{2} < S < {1,8}^{2}\]
\[2,89 < S < 3,24.\]
\[\sqrt{24} + \sqrt{26} < 10\]
\[\left( \sqrt{24} + \sqrt{26} \right)^{2} < 10^{2}\]
\[24 + 2 \cdot \sqrt{24} \cdot \sqrt{26} + 26 < 100\]
\[2 \cdot \sqrt{24} \cdot \sqrt{26} < 100 - 50\]
\[2 \cdot \sqrt{24} \cdot \sqrt{26} < 50\]
\[\sqrt{24} \cdot \sqrt{26} < 25\]
\[\left( \sqrt{24 \cdot 26} \right)^{2} < 25^{2}\]
\[24 \cdot 26 < 625\]
\[624 < 625\]
\[Что\ и\ требовалось\ доказать.\]