Question

Система уравнений со знаками

Answer 1

a) $x \in (1{,}4; +\infty).$

b) $x \in [-1; 6].$

c) $x \in (-2; 4{,}4).$

d) $x = 3.$

Объяснение:

a) $\left \{ {{x-1{,}4 0;} \atop {-5x < 20.}} \right. \Rightarrow \left \{ {{x 1{,}4;} \atop {x -\frac{20}{5}.}} \right. \Rightarrow \left \{ {{x 1{,}4;} \atop {x -4.}} \right. \\\\x \in (1{,}4; +\infty)\ \ \wedge\ \ x \in (-4; +\infty)\ \Rightarrow\\x \in (1{,}4; +\infty) \cap (-4; +\infty);\\x \in (1{,}4; +\infty).$

b) $\left \{ {{2x+2 \geq 3x - 4;} \atop {4x + 4 \geq x + 1.}} \right. \Rightarrow \left \{ {{-x \geq -6;} \atop {3x \geq -3.}} \right. \Rightarrow \left \{ {{x \leq 6;} \atop {x \geq -1.}} \right.\\\\x \in (-\infty; 6]\ \ \wedge\ \ x \in [-1; +\infty) \Rightarrow\\x \in (-\infty; 6] \cap [-1; +\infty);\\x \in [-1; 6].$

c) $\left \{ {{2 - 6x < 14;} \atop {5x - 21 < 1.}} \right. \Rightarrow \left \{ {{- 6x < 12;} \atop {5x< 22.}} \right. \Rightarrow \left \{ {{x -2;} \atop {x< 4{,}4.}} \right.\\\\x \in (-2; +\infty)\ \ \wedge\ \ x \in (-\infty; 4{,}4) \Rightarrow\\x \in (-2; +\infty) \cap (-\infty; 4{,}4);\\x \in (-2; 4{,}4).$

d) $\left \{ {{14 - (4 + 2x) \geq 1 + x;} \atop {6 - 2x \leq 1 - (x - 2).}} \right. \Rightarrow \left \{ {{10 - 2x \geq 1 + x;} \atop {6 - 2x \leq 3 - x.}} \right. \Rightarrow \left \{ {{-3x \geq -9;} \atop {-x \leq -3.}} \right. \Rightarrow \left \{ {{x \leq 3;} \atop {x \geq 3.}} \right.\\\\x \in (-\infty; 3]\ \ \wedge\ \ x \in [3; +\infty) \Rightarrow\\x \in (-\infty; 3] \cap [3; +\infty);\\x \in [3; 3];\\x = 3.$