решите неравенства: IXI БОЛЬШЕ 5 IXI БОЛЬШЕ РАВНО 5 IXI МЕНЬШЕ -5 IXI МЕНЬШЕ РАВНО 0 IXI...

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temichpro_zn · Answer 1 · 2018-02-07T06:30:57+0000

|x|>5 что такое модуль: |x|==0} \atop {-x, x<0}} \right." alt="\left \{ {{x, x>=0} \atop {-x, x<0}} \right." align="absmiddle" class="latex-formula">

=0} \atop {x>5}} \right." alt="\left \{ {{x>=0} \atop {x>5}} \right." align="absmiddle" class="latex-formula">

$\cup$

$\left \{ {{x<0} \atop {x<-5}} \right.$

=0} \atop {x \exists (5;+\infty)}} \right." alt="\left \{ {{x>=0} \atop {x \exists (5;+\infty)}} \right." align="absmiddle" class="latex-formula">

$\cup$

$\left \{ {{x<0} \atop {x \exists (-\infty;-5)}} \right.$

x $\exists$ (-;-5) $\cup$ (5;+).

Ответ: (-\infty;-5) $\cup$ (5;+\infty).

Аналогично с остальными:

|x|>=5

=0} \atop {x>=5}} \right." alt="\left \{ {{x>=0} \atop {x>=5}} \right." align="absmiddle" class="latex-formula">

$\cup$

$\left \{ {{x<0} \atop {x<=-5}} \right.$

=0} \atop {x \exists [5;+\infty)}} \right." alt="\left \{ {{x>=0} \atop {x \exists [5;+\infty)}} \right." align="absmiddle" class="latex-formula">

$\cup$

$\left \{ {{x<0} \atop {x \exists (-\infty;-5]}} \right.$

x (-<</var>;-5][5;+).

...

|x|<-5</p>

По определению, модуль - неотрицательное число, значит х э пустое множество (перечеркнутый круг).

|x|<=0</p>

По выше сказаному определяем, что х=0.

|x|>-5

Если |x|>=0, тогда

=0} \atop {|x|>-5}} \right." alt="\left \{ {{|x|>=0} \atop {|x|>-5}} \right." align="absmiddle" class="latex-formula">

|x|>=0

x (-;+).

|2х|<=6</p>

=0} \atop {2x<=6}} \right." alt="\left \{ {{2x>=0} \atop {2x<=6}} \right." align="absmiddle" class="latex-formula">

$\cup$

=-6}} \right." alt="\left \{ {{2x<0} \atop {2x>=-6}} \right." align="absmiddle" class="latex-formula">

=0} \atop {x<=3}} \right." alt="\left \{ {{x>=0} \atop {x<=3}} \right." align="absmiddle" class="latex-formula">

$\cup$

=-3}} \right." alt="\left \{ {{x<0} \atop {x>=-3}} \right." align="absmiddle" class="latex-formula">

=0} \atop {x \exists [0;3]}} \right." alt="\left \{ {{x>=0} \atop {x \exists [0;3]}} \right." align="absmiddle" class="latex-formula">

$\cup$

$\left \{ {{x<0} \atop {x \exists [-3;0)}} \right.$

x [-3;3].

Ответ: [-3;3]