2x^2 + x - 3 < 0 2x^2 + 3x [latex]geq[/latex] 2 6(1 - x^2) [latex]leq[/latex] 5x 1 - 4x < -4x^2 25x^2 [latex]geq[/latex] -8(5x +2) 6x - 4 > x(1 - 3x)

[latex]2x^{2}+x-3<0 \ D=1-4*2*(-3)=1+24=25 \ sqrt{D}=5 \ x_{1}=frac{-1-5}{4}=frac{-6}{4}=-frac{3}{2} \ x_{2}=frac{-1+5}{4}=frac{4}{4}=1 \ a>0 \ x in (-frac{3}{2};1)[/latex]   [latex]2x^{2}+3xgeq2 \ 2x^{2}+3x-2geq0 \ D=9-4*2*(-2)=9+16=25 \ sqrt{D}=5 \ x_{1}=frac{-3-5}{4}=frac{-8}{4}=-2 \ x_{2}=frac{-3+5}{4}=frac{2}{4}=frac{1}{2} \ a>0 \ [/latex] [latex]x in (-oo;-2>UU0 \ x in do zbioru pustego[/latex]   [latex]25x^{2}geq-8(5x+2) \ 25x^{2}geq-40x-16 \ 25x^{2}+40x+16geq0 \ D=1600-4*25*16=0 \ x_{0}=frac{-40}{50}=-frac{4}{5}=-0,8 \ a>0 \ x in R[/latex]   [latex]6x-4>x(1-3x) \ 6x-4>x-3x^{2} \ 3x^{2}+5x-4>0 \ D=25-4*3*(-4)=73 \ sqrt{D}=sqrt{73} \ x_{1}=frac{-5-sqrt{73}}{6} \ x_{2}=frac{-5+sqrt{73}}{6} \ a>0 \ [/latex]   [latex]x in (-oo;frac{-5-sqrt{73}}{6})U(frac{-5+sqrt{73}}{6};+oo)[/latex]    

2x²+x-3<0 2x²-2x+3x-3<0 2x(x-1)+3(x-1)<0 (2x+3)(x-1)<0 2x+3=0 2x=-3 x=-3/2 ∨ x=1 x∈(-3/2,1)  ----------------------- 2x²+3x≥2 2x²+3x-2≥0 Δ=3²-4*2*(-2) Δ=9+16 Δ=25 √Δ=5   x₁=(-3-5)/(2*2) x₁=-8/4 x₁=-2   x₂=(-3+5)/(2*2) x₂=2/4 x₂=½   x∈(-∞,-2>u<½,∞)  -------------------------- 6(1 - x²)≤5x 6-6x²≤5x 6x²+5x-6≥0 Δ=5²-4*6*(-6) Δ=25+144 Δ=169 √Δ=13   x₁=(-5-13)/(2*6) x₁=-18/12 x₁=-3/2   x₂=(-5+13)/(2*6) x₂=8/12 x₂=2/3   x∈(-∞,-3/2>u<2/3,∞)  ------------------------------- 1 - 4x < -4x² 4x²-4x+1<0 (2x-1)²<0 ⇒ brak rozwiązania ------------------------------- 25x²≥-8(5x +2) 25x²≥-40x-16 25x²+40x+16≥0 (5x+4)²≥0 x∈R  ---------------------------------- 6x - 4 > x(1 - 3x) 6x-4>x-3x² 3x²+5x-4>0 Δ=5²-4*3*(-4) Δ=25+48 Δ=73 √Δ=√73   x₁=(-5-√73)/(2*3) x₁=-⅙(5+√73)   x₂=(-5+√73)/(2*3) x₂=-⅙(5-√73)   x∈(-∞,-⅙(5-√73))u(-⅙(5+√73),∞)        

Rozwiaz nierownosci 6(3x-2)-(4-2x) [latex] geq [/latex] 8+6x 2/3(2x-3) [latex] leq [/latex] (3x-1):2 (2x-1):2-(3y-1):3 [latex] leq [/latex] 1+(x-1):4 2/3x -0,75 [latex] geq [/latex] 1/2(x-2)+0,25x

Rozwiaz nierownosci 6(3x-2)-(4-2x) [latex] geq [/latex] 8+6x 2/3(2x-3) [latex] leq [/latex] (3x-1):2 (2x-1):2-(3y-1):3 [latex] leq [/latex] 1+(x-1):4 2/3x -0,75 [latex] geq [/latex] 1/2(x-2)+0,25x...

Rozwiąż równania   a) 3x-(10+x)=8 b) (5+x)(x-3)=[latex]x^2[/latex]-2 c) 2x+5>3x+6 d) 0,4x+6[latex]leq[/latex]0,15x+5 e) 7x-(2x+5)=15 f) (x+2)(x-3)=[latex]x^2[/latex]+4 g) 4x-6<5x+2 h) 0,25x-5[latex]geq[/latex]0,4x+1

Rozwiąż równania   a) 3x-(10+x)=8 b) (5+x)(x-3)=[latex]x^2[/latex]-2 c) 2x+5>3x+6 d) 0,4x+6[latex]leq[/latex]0,15x+5 e) 7x-(2x+5)=15 f) (x+2)(x-3)=[latex]x^2[/latex]+4 g) 4x-6<5x+2 h) 0,25x-5[latex]geq[/latex]0,4x+1...