a) 3( 2x -1) + 5x = 2- [ 4x - (1 - 2x)] 6x-3+5x=2-4x+1-2x 17x=6 x=17/6 b) x ( x +1) - ( x² + 1) < 2 ( -x + 3 ) x²+x-x²-1<-2x+6 3x<7 x<7/3 c){ 3x - 2y = 8 2x + y = 3 /*2 3x-2y=8 4x+2y=6 ---------------------- 7x=14 x=2 d) x² + 4x - 12 = 0 x²+4x=12 e) 2x² + 10x - 12 ≤ 0 2x²+10x≤12 f) x+3 4x 2x -1 ←→ + →← = ←→→ + 2 /*6 2 3 6 3x+9+8x=2x-1+2 9x=-8 x=8/9
a) 3( 2x -1) + 5x = 2- [ 4x - (1 - 2x)] 6x - 3 + 5x = 2 - (4x - 1 + 2x) 11x - 3 = 2 - 4x + 1 - 2x 11x + 4x + 2x = 2 + 1 + 3 17x = 6 x = 6/17 b) x ( x +1) - ( x² + 1) < 2 ( -x + 3 ) x² + x - x² - 1< - 2x + 6 x + 2x < 6 + 1 3x < 7 x < 7/3 c){ 3x - 2y = 8 { 2x + y = 3 mnożymy przez 2 3x - 2y = 8 4x + 2y = 6 dodajemy stronami 3x + 4x - 2y + 2y = 8 + 6 7x = 14 x = 14/7 = 2 d) x² + 4x - 12 = 0 Δ = 16 + 48 Δ = 64 √Δ = √64 = 8 x1 = - 4 - 8/2 = - 12/2 = - 6 x2 = - 4 + 8/2 = 4/2 = 2 e) 2x² + 10x - 12 ≤ 0 Δ = 100 + 96 = 196 √Δ = √196 = 14 x1 = - 10 - 14/2 = - 24/2 = - 12 x2 = - 10 + 14/2 = + 4/2 = 2 (x - x1)(x - x2)≤0 x - x1 ≤ 0 i x - x2 ≥ 0 lub x - x1≥ 0 i x - x2 ≤ 0 x ≤ 12 i x ≥ - 2 lub x ≥ 12 i x ≤ - 2 odp x ≤ 12 i x ≥ - 2 jest to przedział ( - 2 , 12)
