1.
(x-6)(4x+7) ≤0
9-x
{9-x≠0
{(x-6)(4x+7)(9-x)≤0
x≠9
(x-6)(4x+7)(9-x)≤0
-(x-9)(x-6)*4(x+⁷/₄) ≤0
(x-9)(x-6)(x+⁷/₄) ≥0
x=9 x=6 x=-⁷/₄
- + - +
-------- -⁷/₄ ----------- 6 ------------- 9 ---------------
\\\\\\\\\\\\\ \\\\\\\\\\\\\\\\
x∈[-⁷/₄; 6] U (9; +∞)
2.
x²-3x+2 >0
6+3x
{6+3x≠0
{(x²-3x+2)(6+3x) >0
6+3x≠0
3x≠-6
x≠-2
(x²-3x+2)(6+3x)>0
Разложим на множители:
x²-3x+2=0
D=9-8=1
x₁=3-1=1
2
x₂=3+1=2
2
x²-3x+2=(x-1)(x-2)
3(x+2)(x-1)(x-2)>0
(x+2)(x-1)(x-2)>0
x=-2 x=1 x=2
- + - +
------------ -2 -------------- 1 ------------ 2 -------------
\\\\\\\\\\\\\\ \\\\\\\\\\\\\\\
x∈(-2; 1) U (2; +∞)
3.
3x²+4x >0
9-x
{9-x≠0
{(3x²+4x)(9-x)>0
9-x≠0
x≠9
(3x²+4x)(9-x)>0
-3x(x+⁴/₃)(x-9)>0
x(x+⁴/₃)(x-9)<0<br>x=0 x=-⁴/₃ x=9
- + - +
------ -⁴/₃ --------- 0 ------------- 9 -----------
\\\\\\\\\ \\\\\\\\\\\\\\
x∈(-∞; -⁴/₃) U (0; 9)
4.
8-32x² >0
x-10
{x-10≠0
{(8-32x²)(x-10)>0
x≠10
(8-32x²)(x-10)>0
-8(4x²-1 )(x-10)>0
(2x-1)(2x+1)(x-10)<0<br>2(x-0.5)*2(x+0.5)(x-10)<0<br>(x-0.5)(x+0.5)(x-10)<0<br>x=0.5 x=-0.5 x=10
- + - +
------- -0.5 --------- 0.5 ---------- 10 --------------
\\\\\\\\\ \\\\\\\\\\\\\
x∈(-∞; -0,5) U (0.5; 10)