Rozwiąż równanie wymierne a)3-x / 5x-11 <0 b)2x /3x+2 <2 c) 2x−1 /3x+4 > −3/4

[latex]a) frac{3-x}{5x-11} extless 0 / cdot (5x-1)^2 Zal. 5x-11 eq 0 \ mathrm{ (3-x)(5x-11) extless 0 5x eq 11} \ mathrm{ 3-x=0 vee 5x-11=0 x eq frac{11}{5} } \ mathrm{ x=3 vee x= frac{11}{5} } \ mathbf{ x in (- infty,frac{11}{5}) vee ( 3 , + infty)}[/latex] [latex]b) frac{2x}{3x-2} extless 2 mathrm{ Zal. x eq frac{2}{3} } \ mathrm{ frac{2x}{3x-2}-2 extless 0} \ mathrm{ frac{2x}{3x-2}- frac{2(3x-2)}{3x-2}} extless 0 \ mathrm{ frac{2x-6x+4}{3x-2} extless 0} \ mathrm{ frac{-4x+4}{3x-2} extless 0 / cdot (3x-2)^2} \ mathrm{ (-4x+4)(3x-2) extless 0} \ mathrm{ -4x+4=0 vee 3x-2=0} \ mathrm{ x=1 vee x= frac{2}{3} } [/latex]        [latex]mathbf{ x in (- infty, frac{2}{3}) vee (1, + infty) } [/latex] [latex]mathrm{c) frac{2x-1}{3x+4} extgreater - frac{3}{4} Zal. x eq - frac{4}{3} } \ mathrm{ frac{2x-1}{3x+4}+ frac{3}{4} extgreater 0}\ mathrm{ frac{4(2x-1)}{4(3x+4)}+ frac{3(3x+4)}{4(3x+4)} extgreater 0 } \ mathrm{ frac{8x-4+9x+12}{4(3x+4)} extgreater 0 / cdot [4(3x+4)]^2 } \ mathrm{ 16(3x+4)(17x+8) extgreater 0} \ mathrm{ 3x+4=0 vee 17x+8=0} \ mathrm{ x=- frac{4}{3} vee x=- frac{8}{17} } [/latex]           [latex]mathbf{ x in ( - infty, - frac{4}{3}) vee (- frac{8}{17}, + infty ) }[/latex]

a) Założenie: 5x-11≠0 5x≠11 x≠11/5 x≠2 i 1/5 [latex] frac{3-x}{5x-11} extless 0 /*(5x-11)^{2} \ (3-x)(5x-11) extless 0 \ 15x-33-5x^{2}+11x extless 0 \ -5x^{2}+26x-33 extless 0 [/latex] Δ=676-660=16 [latex] x_{1} = frac{-26-4}{-10}=3 \ x_{2}= frac{-26+4}{-10}= 2 frac{2}{10} =2frac{1}{5} [/latex] x∈[latex](2 frac{1}{5},3) [/latex] b) Założenie: 3x+2≠0 3x≠-2 x≠-2/3 [latex] frac{2x}{3x+2} extgreater 2 \ frac{2x}{3x+2}-2 extgreater 0/*(3x+2)^{2} \ 2x(3x+2)-2(3x+2)^{2} extgreater 0 \ 6x^{2}+4x-2(9x^{2}+12x+4) extgreater 0 \ 6x^{2}+4x-18x^{2}-24x-8 extgreater 0 \ -12x^{2}-20x-8 extgreater 0[/latex] Δ=400-384=16 [latex] x_{1}= frac{20-4}{-24}=- frac{16}{24}=- frac{2}{3} \ x_{2}= frac{20+4}{-24}=-1 [/latex] x∈[latex](- frac{2}{3},-1) [/latex] c) Założenie: 3x+4≠0 3x≠-4 x≠-4/3 [latex] frac{2x-1}{3x+4} extgreater - frac{3}{4} \ frac{2x-1}{3x+4}+frac{3}{4} extgreater 0/*4(3x+4)^{2} \ (2x-1)(3x+4)+3(3x+4)^{2} extgreater 0 \ 6x^{2}+8x-3x-4+3(9x^{2}+24x+16) extgreater 0 \ 6x^{2}+5x-4+27x^{2}+72x+48 extgreater 0 \ 33x^{2}+77x+44 extgreater 0[/latex] Δ=5929-5808=121 [latex] x_{1}= frac{-77-11}{66}=- frac{4}{3} \ x_{2}= frac{-77+11}{66}=-1 [/latex] x∈(-∞, -4/3)u(-1,∞)