Question

Zad1. rozwiąż podane równania:
a)3(2x-1)+5x=2-[1-2x)]
b) (x+4)²+14=(X-2)²+2
C)(2x-3)²=(1-2x)²+2(4-4x)
d)(4x-3)(4x+3)-(x+1)²=15(x-2)²-10-2x
e)x(x-2)-(x+1)(x-3)=1+2x
zad2. rozwiaz rownania:
a) (x-3)=2
b) (5x-1)=9
c) (3x-4)=5
d)(1-2x)=3
e)3-(5-3x)=4
f) 2(x+6)-1=0
zad3 rozwiaz podane nierównosci
a) x(x+1)-(x²+1)<2(-x+3)
b)(2x-3)(2x+3)-4(4x-2)>(2x-5)²
c)5(x-1)²>2(x²+4)+x(3x+4)+x

Answer 1

Zad 1:)
a) 3(2x-1)+5x=2-(1-2x)
6x-3+5x=2-1+2x
6x+5x-2x=2-1+3
9x=6/:9
x=2/3

b) (x+4)²+14=(x-2)²+2
x²+8x+16+14=x²-4x+4+2
x²-x²+8x+4x=4+2-14-16
12x=-24/12
x=-2

Answer 2

Zad1.
a)3(2x-1)+5x=2-[1-2x)]
6x-3+5x = 2-1+2x
11x-3 = 2x+1 /-2x +3
9x = 4 /:9
x = 4/9


b) (x+4)²+14=(X-2)²+2
x²+8x+16+14 = x²-4x+4+2 /-x²
8x+30 = -4x+6 /+4x -30
12x = -24 /:12
x = -2


C)(2x-3)²=(1-2x)²+2(4-4x)
4x²-12x+9 = 1-4x+4x²+8-8x /-4x²
-12x+9 = -12x+9
brak rozwiązań


d)(4x-3)(4x+3)-(x+1)²=15(x-2)²-10-2x
16x²-9-x²-2x-1 = 15x²-60x-60-10-2x /-15x²
-2x-10 = -62x-70 /+62x +10
60x = -60 /:60
x = -1


e)x(x-2)-(x+1)(x-3)=1+2x
x²-2x-x²+3x-x+3 = 1+2x
3 = 1+2x
2x = -2
x = -1


zad2. rozwiaz rownania:
a) (x-3)=2
x-3 = 2
x = 5

b) (5x-1)=9
5x-1 = 9
5x = 10 /:5
x = 2

c) (3x-4)=5
3x-4 = 5
3x = 9 /:3
x = 3

d)(1-2x)=3
1-2x = 3
-2x = 2 /:(-2)
x = -1

e)3-(5-3x)=4
3-5-3x = 4
-3x = 6 /:(-3)
x = -2


f) 2(x+6)-1=0
2x+12-1 = 0
2x = -11 /:2
x = -5,5



zad3 rozwiaz podane nierównosci
a) x(x+1)-(x²+1)<2(-x+3)
x²+x-x²-1 < -2x+6
x-1 < -2x+6 /+1 +2x
3x < 7 /:3
x < 2 i 1/3


b)(2x-3)(2x+3)-4(4x-2)>(2x-5)²
4x²+6x-6x-9-16x+8 > 4x²-20x+25 /-4x²
-16x-1 > -20x+25 /+20x +1
4x > 26 /:4
x > 6,5



c)5(x-1)²>2(x²+4)+x(3x+4)+x
5x²-10x+5 > 2x²+8+3x²+4x+x /-5x²
-10x+5 > 5x+8 /+10x -8
-3 > 15x /:15
-1/5 > x