Сызықтық теңсіздіктер (Рустюмова 1.5.1)

Шешуі: $$ - 2x + 5x \lt 12 - 3$$ $$3x \lt 9$$ $$x \lt 3$$ Жауабы: 2

Шешуі: $$x - 8 \ge 2x + 1 + 7$$ $$x - 2x \ge 1 + 7 + 8$$ $$ - x \ge 16$$ $$x \le - 16$$ Жауабы: -16

Шешуі: $${x^2} + 3x \gt {x^2} + 3x + x + 3$$ $$ - x \gt 3$$ $$x \lt - 3$$ Жауабы: -4

Шешуі: $$9(9x + 2) - 10(10x - 2) \gt 2 \cdot 90$$ $$81x + 18 - 100x + 20 \gt 180$$ $$ - 19x \gt 180 - 20 - 18$$ $$ - 19x \gt 142$$ $$x \lt - \frac{{142}}{{19}}$$ $$x \lt - 7\frac{9}{{19}}$$ Жауабы: -8

Шешуі: $$14(3x - 1) - 35(x + 1) \lt 70 - 10x$$ $$42x - 14 - 35x - 35 \lt 70 - 10x$$ $$42x - 35x + 10x \lt 70 + 14 + 35$$ $$17x \lt 119$$ $$x \lt 7$$ Жауабы: 6

Шешуі: $$3x + 3 \lt 5x + 5 - 2$$ $$3x - 5x \lt 5 - 2 - 3$$ $$ - 2x \lt 0$$ $$x \gt 0$$ Жауабы: 1

Шешуі: $$3(3x + 5) - 12 \le 4(x - 2) + 12x$$ $$9x + 15 - 12 \le 4x - 8 + 12x$$ $$9x - 4x - 12x \le - 8 - 15 + 12$$ $$ - 7x \le - 11$$ $$x \ge \frac{{11}}{7}$$ $$x \ge 1\frac{4}{7}$$ Жауабы: 2

Шешуі: $$2(x - 3) - 1 \gt 3(x - 2) - 4(x + 1)$$ $$2x - 7 \gt - x - 10$$ $$2x + x \gt - 10 + 7$$ $$3x \gt - 3$$ $$x \gt - 1$$ Жауабы: 0

Шешуі: $${x^2} + x \lt {x^2} + 5x + 5$$ $$x - 5x \lt 5$$ $$ - 4x \lt 5$$ $$x \gt - \frac{5}{4}$$ $$x \gt - 1\frac{1}{4}$$ Жауабы: -1

Шешуі: $$4(x + 4) - 7(x + 7) \lt - 3 \cdot 28$$ $$4x + 16 - 7x - 49 \lt - 84$$ $$4x - 7x \lt - 84 - 16 + 49$$ $$ - 3x \lt - 51$$ $$x \gt 17$$ Жауабы: 18

Шешуі: $$2 + 5 \lt 3x \lt 4 + 5$$ $$7 \lt 3x \lt 9$$ $$\frac{7}{3} \lt x \lt 3$$ $$2\frac{1}{3} \lt x \lt 3$$ Жауабы: $\emptyset$

Шешуі: $$ - 2 - 4 \le - 2x \le 2 - 4$$ $$ - 6 \le - 2x \le - 2$$ $$3 \ge x \ge 1$$ $$1 \le x \le 3$$ Жауабы: 1

Шешуі: $$\left\{ \begin{array}{l}3 - x \gt x\\3 - x \le 11\end{array} \right. \Rightarrow \left\{ \begin{array}{l} - x - x \gt - 3\\ - x \le 11 - 3\end{array} \right. \Rightarrow $$ $$ \Rightarrow \left\{ \begin{array}{l} - 2x \gt - 3\\ - x \le 8\end{array} \right. \Rightarrow \left\{ \begin{array}{l}x \lt \frac{3}{2}\\x \ge - 8\end{array} \right.$$ Жауабы: -8

Шешуі: $$\left\{ \begin{array}{l}12{x^2} - 12{x^2} - 2x + 18x + 3 \gt x\\25{x^2} - 1 - 25{x^2} \gt x - 6\end{array} \right. \Rightarrow \left\{ \begin{array}{l} - 2x + 18x - x \gt - 3\\ - x \gt - 6 + 1\end{array} \right. \Rightarrow $$ $$ \Rightarrow \left\{ \begin{array}{l}15x \gt - 3\\ - x \gt - 5\end{array} \right. \Rightarrow \left\{ \begin{array}{l}x \gt - \frac{1}{5}\\x \lt 5\end{array} \right.$$ $$ x\in (-\frac{1}{5};\, 5) $$ Жауабы: 0

Шешуі: $$\left\{ {\begin{array}{*{20}{l}}{3x - 8x \lt 6 + 4}\\{2x - 5x \gt - 4 + 1}\\{11x - 15x \lt 3 + 9}\end{array}} \right. \Rightarrow \left\{ {\begin{array}{*{20}{l}}{ - 5x \lt 10}\\{ - 3x \gt - 3}\\{ - 4x \lt 12}\end{array} \Rightarrow \left\{ {\begin{array}{*{20}{l}}{x \gt - 2}\\{x \lt 1}\\{x \gt - 3}\end{array}} \right.} \right.$$ $$x \in \left( { - 2;1} \right)$$ Жауабы: -1

Шешуі: $$\left\{ {\begin{array}{*{20}{l}}{5(7 - x) - 30 \le 2(3 + 4x) - 40}\\{5x + 15(4 - x) \gt 6(4 - x)}\end{array}} \right. \Rightarrow \left\{ \begin{array}{l}35 - 5x - 30 \le 6 + 8x - 40\\5x + 60 - 15x \gt 24 - 6x\end{array} \right. \Rightarrow $$ $$ \Rightarrow \left\{ \begin{array}{l} - 13x \le - 39\\ - 4x \gt - 36\end{array} \right. \Rightarrow \left\{ \begin{array}{l}x \ge 3\\x \lt 9\end{array} \right.$$ $$x \in \left[ {3;9} \right)$$ Жауабы: 3

Шешуі: $${\begin{array}{*{20}{l}}{1,2x + 7 \lt 2x - 3,6}\\{5x - 9x \gt - 63 - 17}\end{array} \Rightarrow \left\{ {\begin{array}{*{20}{l}}{ - 0,8x \lt - 10,6}\\{ - 4x \gt - 80}\end{array} \Rightarrow \left\{ {\begin{array}{*{20}{l}}{x \gt 13,25}\\{x \lt 20}\end{array}} \right.} \right.}$$ $$x \in \left( {13,25;\,\,20} \right)$$ Жауабы: 14

Шешуі: $$\left\{ \begin{array}{l}33x \gt 22 - 2x + 13\\3x + 12(x - 7) \lt 2(3x - 20)\end{array} \right. \Rightarrow \left\{ \begin{array}{l}33x + 2x \gt 22 + 13\\3x + 12x - 84 \lt 6x - 40\end{array} \right. \Rightarrow $$ $$\left\{ \begin{array}{l}35x \gt 35\\3x + 12x - 6x \lt - 40 + 84\end{array} \right. \Rightarrow \left\{ \begin{array}{l}x \gt 1\\9x \lt 44\end{array} \right. \Rightarrow \left\{ \begin{array}{l}x \gt 1\\x \lt 4\frac{8}{9}\end{array} \right.$$ $$x \in \left( {1;4\frac{1}{9}} \right)$$ Жауабы: 2+3+4=9

Шешуі: $$\left\{ {\begin{array}{*{20}{l}}{6(x - 1) - 4(x - 2) \ge 3(x - 3) - 12x}\\{ - 0,5x - x \gt - 4 - 1}\end{array}} \right. \Rightarrow \left\{ {\begin{array}{*{20}{l}}{6x - 6 - 4x + 8 \ge 3x - 9 - 12x}\\{ - 1,5x \gt - 5}\end{array}} \right. \Rightarrow $$ $$ \Rightarrow \left\{ {\begin{array}{*{20}{l}}{11x \ge - 11}\\{x \lt \frac{{10}}{3}}\end{array}} \right. \Rightarrow \left\{ {\begin{array}{*{20}{l}}{x \ge - 1}\\{x \lt \frac{{10}}{3}}\end{array}} \right.$$ $$x \in \left[ {1;\frac{{10}}{3}} \right)$$ Жауабы: -1+1+2+3=5

Шешуі: $$\left\{ \begin{array}{l}12x - 6(x - 1) - 4(x + 2) \le 3(x - 3)\\1,5x - x \lt 5,05\end{array} \right. \Rightarrow $$ $$ \Rightarrow \left\{ \begin{array}{l}12x - 6x + 6 - 4x - 8 \le 3x - 9\\0,5x \lt 5,05\end{array} \right. \Rightarrow \left\{ \begin{array}{l} - x \le - 7\\x \lt 10,5\end{array} \right. \Rightarrow \left\{ \begin{array}{l}x \ge 7\\x \lt 10,5\end{array} \right.$$ $$x \in \left[ {7;\,\,10,5} \right)$$ Жауабы: 7+8+9+10=34

Шешуі: $$\left\{ {\begin{array}{*{20}{l}}{3 - 2x \le 5(x - 2) + 3x}\\{1 - 3x \ge 4(5x - 1) - 21x}\end{array}} \right. \Rightarrow \left\{ {\begin{array}{*{20}{l}}{3 - 2x \le 5x - 10 + 3x}\\{1 - 3x \ge 20x - 4 - 21x}\end{array}} \right. \Rightarrow $$ $$ \Rightarrow \left\{ {\begin{array}{*{20}{l}}{ - 2x - 5x - 3x \le - 10 - 3}\\{ - 3x - 20x + 21x \ge - 4 - 1}\end{array}} \right. \Rightarrow \left\{ {\begin{array}{*{20}{l}}{ - 10x \le - 13}\\{ - 2x \ge - 5}\end{array}} \right. \Rightarrow \left\{ {\begin{array}{*{20}{l}}{x \ge 1,3}\\{x \le 2,5}\end{array}} \right.$$ $$x \in \left[ {1,3;\,\,2,5} \right]$$ Жауабы: 2