403.
1) (8-4x)/(3x² - x -4) ≤4;
4(2-x)/(3x² - x -4) ≤ 4;
(2-x)/(3x² - x -4) ≤ 1;
1 -(2-x)/(3x² - x -4) ≥ 0 ; *** [ 3x² - x -4 =3(x-x₁)(x-x₂) =3(x+4/3)(x -1) ] ***
(3x² -x -4 -2+x)/(3x² - x -4 ≥ 0;
3(x² -2)/(3x² -x -4) ≥ 0;
3(x +√2)(x-√2)/3(x+4/3)(x-1)≥0;
(x +√2)(x -√2) /(x+4/3)(x-1)≥0;
{ (x +√2) (x+4/3)(x-1)(x -√2) ≥0; x≠-4/3 ;x≠1.
методом интервалов :
+ - + - +
------------- - √2 ------- -4/3 -------- 1 -------- √2 -----------
ответ : x ∈ (-∞ ; -√2 ] U ( -4/3; 1) U [√2;∞) .
2) (- 33x -9)/(4-11x-7x²) ≤ 3;
-3(11x +3)/(-(7x²+11x -4)≤3;
(11x +3)/(7x²+11x -4)≤1 ;
1 - (11x +3)/(7x²+11x -4) ≥ 0 ;
(7x²+11x -4 -11x-3)/(7x²+11x -4) ≥ 0 ;
7(x+1)(x-1)/(7x² +11x -4) ≥ 0 ;
7(x+1)(x-1)/7(x+(11+√233)/14)(x -(√233 -11)/14) ≥ 0 ;
*** [ 7x² +11x -4 =7(x+(11+√233)/14)(x -(√233 -11)/14) ] ***
(x+1)(x-1)/(x+(11+√233)/14)(x -(√233 -11)/14) ≥ 0 ;
{(x+(11+√233)/14)(x+1)(x -(√233 -11)/14)(x-1) ≥ 0 ;x ≠ -(11+√233)/14 ;;x ≠ (√233 -11)/14.
+ - + - +
-------- -(11+√233)/14 ----- -1 -------- (√233 -11)/14 ----- 1 ---------------
ответ : x∈ (-∞ ; -(11+√233)/14 ) U [ -1;√233 -11)/14 ) U [ 1 ;∞).