2.
{3(x+3)-x<12<br>{x/3 - (2x-3)/4 >2
3(x+3)-x<12<br>3x+9-x<12<br>2x<12-9<br>2x<3<br>x<1.5<br>
x/3 - (2x-3)/4 >2
x - 2x-3 - 2 >0
3 4
4x - 3(2x-3)-2*12 >0
4x - 6x+9 -24 >0
-2x -15 >0
-2x>15
x<-7.5<br>\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
---------- -7.5 -------------- 1.5 -------------
\\\\\\\\\\\
x< -7.5
x∈(-∞; -7,5)
3.
5 >2
x
x≠0
5 - 2 >0
x
5-2x >0
x
x(5-2x)>0
-2x(x-⁵/₂) >0
x(x - ⁵/₂) <0<br>x=0 x=2.5
+ - +
----------- 0 -------------- 2.5 ----------------
\\\\\\\\\\\\\\\
x∈(0; 2,5)
х=1; 2 - целые решения неравенства
4.
у=√(х - 8/(х-2))
х - 8 ≥ 0
х-2
х≠2
х(х-2) -8 ≥0
х-2
х² -2х -8 ≥ 0
х-2
Разложим х² -2х-8 на множители:
х² -2х-8=0
D=4+32=36
x₁=2-6 = -2
2
x₂ = 2+6 =4
2
x²-2x-8=(x+2)(x-4)
(x+2)(x-4) ≥ 0
x-2
(x+2)(x-4)(x-2) ≥0
x=-2 x=4 x=2
- + - +
-------- -2 ----------- 2 ----------- 4 --------------
\\\\\\\\\\\ \\\\\\\\\\\\\
x∈[-2; 2)U[4; +∞)
D(y)= [-2; 2) U [4; +∞) - область определения функции.