Question

Zad.1.
Rozwiąż równania.
a. (4x+3)-(3x+5)=(2x+6)+(2x+7)
b. 2(x+8)-x=4x+5
c. 2x+ 3x/4 = 57+ 5x/7
d. (7x-13)/12 = (x-5)/2 + (x-4)/8

Zad.2.
Rozwiąż nierówności.
a. 29x+27-8x < 28 +7x - 105
b. (x-3)/4 + (x-4)/3 ≤ (x-5)/2 + (x-4)/8
c. (4x-3)/2 - (5-2x)/3 - (3x-4)/3 < 5


Punkty dam tylko za rozwiazanie dwoch zadan!

Answer 1

Zadanie 1
a. (4x+3)-(3x+5)=(2x+6)+(2x+7)
4x+3-3x-5=2x+6+2x+7
4x-3x-2x-2x=6+7+5-3
-3x=15/:(-3)
x=-5
b. 2(x+8)-x=4x+5
2x+16-x=4x+5
2x-x-4x=5-16
-3x=-11/:(-3)
x= 3 2/3
c. 2x+ 3x/4 = 57+ 5x/7
2x+3x/4-5x/7=57
2x+21/28x-20/28x=57
2x+1/28x=57
2 1/28x=57
57/28x=57 /* 28/57
x=28
d. (7x-13)/12 = (x-5)/2 + (x-4)/8
7x/12-13/12=x/2-5/2+x/8-4/8
7x/12-x/2-x/8=-5/2-4/8+13/12
14/24x-12/24x-3/24x=-60/24-12/24+26/24
-1/24x=-46/24/*(-24)
x=46
zadanie 2
a. 29x+27-8x < 28 +7x - 105
29x-8x-7x<28-105-27
14x<-104/:14
x< -7 6/14
x< -7 3/7
b. (x-3)/4 + (x-4)/3 ≤ (x-5)/2 + (x-4)/8
x/4-3/4+x/3-4/3 ≤ x/2-5/2+x/8-4/8
x/4+x/3-x/2-x/8 ≤ -5/2-4/8+3/4+4/3
6x/24+8x/24-12x/24-3x/24 ≤ -60/24-12/24+18/24+32/24
-x ≤ -22 /:(-1)
x ≥ 22
c. (4x-3)/2 - (5-2x)/3 - (3x-4)/3 < 5
4x/2-3/2-5/3+2x/3-3x/3+4/3 < 5
4x/2+2x/3-3x/3< 5+3/2+5/3-4/3
12x/6+4x/6-6x/6 < 30/6+9/6+10/6-8/6
10/6x < 41/6 /*6
10x < 41 /:10
x < 4,1