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