Question

A) x/3 + 1 =5/6 +x/2
b) 2x-3/4 = 1/2 + x
c) x+2 /9 + x-1/3 +1
d) 2x+3/5 = 2-x/3 +x
e) 3x-5/2 - 5x-1 /10 =0
f) x/2 = 2/5 (4-x ) -4
g) 2x-3x + 5 /4 =-1/4x-1

Answer 1

A) x/3 + 1 = 5/6 + x/2 /*6
2x+6=5+3x
6=5+x
x=1

b) x + 2 /9 + x-1/3= 1 /*9
x+2+3x-3=9
4x-1=9
4x=10
x=10/4= 2½

c)5+3x /4 - 4x + 9 /3=1 3/4
5+3x /4 - 4x+9 /3= 7/4 /*12
15+9x- 16x- 36=21
21-7x=21
-7x=42
x=-6

Answer 2

A) x/3 + 1 =5/6 +x/2 /*6
2x+6=5+3x
-x=-1 /*(-1)
x=1

b) 2x-3/4 = 1/2 + x /*4
8x-3=2+4x
4x=5 /:4
x= 1 1/4
lub jeśli (2x-3)/4
(2x-3)/4=1/2+x /*4
2x-3=2+4x
-2x=5 /:(-2)
x=-2 1/2

c) x+2 /9 + x-1/3 +1 /*9
9x+1+9x-3+9=0
18x=-7 /:18
x= -7/18

lub jeśli (x+2)/9 + (x-1)/3+1=0 /*9
x+2+3x-3+9=0
4x=-8 /:4
x=-2



d) 2x+3/5 = 2-x/3 +x /*15
3(2x+3)=5(2-x)+15x
6x+9=10-5x+15x
-4x=1 /:(-4)
x=-1/4


e) 3x-5/2 - 5x-1 /10 =0 /*10
5(3x-5)-5x-1=0
15x-25-5x-1=0
10x=26 /:10
x= 2 3/5

f) x/2 = 2/5 (4-x ) -4 /*10
5x=4(4-x)-40
5x=16-4x-40
9x=-24 /:9
x= -2 2/3


g) 2x-3x + 5 /4 =-1/4x-1 /*4
8x-12x+5=-x-4
8x-12x+x=-4-5
-3x=-9 /:(-3)
x=3

lub
2x-3x + 5 /4 =-1/4x-1 /*4
8x-12x+5=-4/4x-1 /*(4x-1)
8x(4x-1)-12x(4x-1)+5(4x-1)=-4
32x²-8x-48x²+12+20x-5=-4
-16x²+12x+11=0
Δ=12²-4(-16*11)
Δ=848

√Δ=29√7
x1=(-12-29√7)/-32

x2=(-12+29)/-32