Решите неравенство: 1)|x-3| >=1,8 2)|2-x| >1\3 3)|3-x| <1,2 4) |4+х| <=1,8 5)|0,5-х| >= 3...

Question

Дано ответов: 2

Luluput_zn · Answer 1 · 2018-05-10T06:35:59+0000

1)
$|x-3| \geq 1.8$
$x-3 \geq 1.8$ или    $x-3 \leq -1.8$
$x \geq 1.8+3$ или    $x \leq -1.8+3$
$x \geq 4.8$ или    $x \leq 1.2$

----------[1.2]-----------[4.8]---------------
/////////// //////////////////
$x$ ∈ $(-$ ∞ $;1.2]$ ∪ $[4.8;+$ ∞ $)$

2)
$|2-x|\ \textgreater \ \frac{1}{3}$
$2-x\ \textgreater \ \frac{1}{3}$ или    $2-x\ \textless \ - \frac{1}{3}$
$-x\ \textgreater \ \frac{1}{3}-2$ или    $-x\ \textless \ - \frac{1}{3} -2$
$x\ \textless \ 1 \frac{2}{3}$    или    $x\ \textgreater \ 2 \frac{1}{3}$

----------(1 2/3)-----------(2 1/3)---------------
/////////// //////////////////
$x$ ∈ $(-$ ∞ $;1\frac{2}{3})$ ∪ $(2\frac{2}{3};+$ ∞ $)$

3)
$| 3-x|\ \textless \ 1.2$
$\left \{ {{3-x\ \textless \ 1.2} \atop {3-x\ \textgreater \ -1.2}} \right.$
$\left \{ {{-x\ \textless \ 1.2-3} \atop {-x\ \textgreater \ -1.2-3}} \right.$
$\left \{ {{-x\ \textless \ -1.8} \atop {-x\ \textgreater \ -4.2}} \right.$
$\left \{ {{x\ \textgreater \ 1.8} \atop {x\ \textless \ 4.2}} \right.$

---------(1.8)-----------(4.2)----------
/////////////////
$x$ ∈ $(1.8;4.2)$

4)
$|4+x | \leq 1.8$
$\left \{ {{4+x \leq 1.8} \atop { 4+x \geq -1.8}} \right.$
$\left \{ {{x \leq 1.8-4} \atop { x \geq -1.8-4}} \right.$
$\left \{ {{x \leq -2.2} \atop { x \geq -5.8}} \right.$

----------[-5.8]---------[-2.2]-----------
////////////////
$x$ ∈ $[-5.8;-2.2]$

5)
$|0.5-x| \geq 3$
$0.5-x\geq 3$ или    $0.5-x \leq - 3$
$-x\geq 3-0.5$ или    $-x \leq -3-0.5$
$-x\geq 2.5$ или    $-x \leq -3.5$
$x \leq -2.5$ или $x \geq 3.5$

----------[-2.5]-----------[3.5]---------------
/////////// //////////////////
$x$ ∈ $(-$ ∞ $;-2.5]$ ∪ $[3.5;+$ ∞ $)$

6)
$|6-x | \leq 2.1$
$\left \{ {{ 6-x \leq 2.1} \atop { 6-x \geq -2.1}} \right.$
$\left \{ {{ -x \leq 2.1-6} \atop { -x \geq -2.1-6}} \right.$
$\left \{ {{ -x \leq -3.9} \atop { -x \geq -8.1}} \right.$
$\left \{ {{ x \geq 3.9} \atop { x \leq 8.1}} \right.$

----------[3.9]---------[8.1]-----------
////////////////
$x$ ∈ $[3.9;8.1]$