Odpowiedź:
zad. 3
a)
2x= 5
x= 5 : 2
x= 2,5
spr.
2x= 5
L= 2x= 2* 2,5 = 5
P= 5
5=5
L=P
a + a + a = 9
3a= 9
a= 9 : 3
a= 3
spr.
a + a + a = 9
L= a + a + a= 3+3 + 3= 9
P= 9
9=9
L=P
c * c * c = 27
c³ = 27
c=∛27
c = 3
spr.
c * c * c= 27
L= c * c * c= 3 * 3 * 3= 27
P= 27
27 = 27
L=P
b)
15 - x = 7 i 1/3
-x = 7 i 1/3 - 15
-x = - 7 i 2/3 /*(-1)
x= 7 i 2/3
spr.
15 - x = 7 i 1/3
L= 15 - x= 15 - 7 i 2/3 = 14 i 3/3 - 7 i 2/3 = 7 i 1/3
P = 7 i 1/3
7 i 1/3 = 7 i 1/3
L=P
m - 1 i 5/6 = 2 i 2/3
m = 2 i 2/3 + 1 i 5/6
m = 2 i 4/6 + 1 i 5/6
m = 3 i 9/6
m = 4 i 3/6
spr.
m - 1 i 5/6 = 2 i 2/3
L= m - 1 i 5/6 = 4 i 3/6 - 1 i 5/6 = 3 i 9/6 - 1 i 5/6 = 2 i 4/6 = 2 i 2/3
P= 2 i 2/3
2 i 2/3 = 2 i 2/3
L=P
8 i 5/8 + 1/2b = 15 i 1/4
1/2b = 15 i 1/4 - 8 i 5/8
1/2b = 15 i 2/8 - 8 i 5/8
1/2b = 14 i 10/8 - 8 i 5/8
1/2b = 6 i 5/8
b= 6 i 5/8 : 1/2
b = 53/8 * 2/1
b = 53/4 * 1/1
b = 53/4
b= 13 i 1/4
spr.
8 i 5/8 + 1/2b = 15 i 1/4
L = 8 i 5/8 + 1/2b = 8 i 5/8 + 1/2 * 13 i 1/4 = 8 i 5/8 + 1/2 * 53/4 =
= 8 i 5/8 + 53/8 = 8 i 5/8 + 6 i 5/8 = 14 i 10/8 = 15 i 2/8 = 15 i 1/4
P = 15 i 1/4
15 i 1/4 = 15 i 1/4
L=P
c)
d : 4 = 5 i 1/2
d= 5 i 1/2 * 4
d= 11/2 * 4
d= 11/1 * 2
d= 22/1
d= 22
spr.
d : 4 = 5 i 1/2
L= d : 4= 22 : 4= 22/4= 5 i 2/4= 5 i 1/2
P= 5 i 1/2
5 i 1/2 = 5 i 1/2
L=P
zad.4
a)
2c : 8 = 1 i 1/2
2c = 1 i 1/2 * 8
2c= 3/2 * 8
2c= 3/1 * 4
2c= 12/1
2c= 12
c= 12 : 2
c= 6
spr.
2c : 8 = 1 i 1/2
L= 2c : 8 = 2 * 6 : 8 = 12 : 8 = 12 * 1/8 = 3 * 1/2 = 3/2= 1 i 1/2
P= 1 i 1/2
1 i 1/2 = 1 i 1/2
L=P
3d : 2 = 2 i 1/4
3d= 2 i 1/4 * 2
3d= 9/4 * 2
3d= 9/2 * 1
3d= 9/2
d= 9/2 : 3
d= 9/2 * 1/3
d= 3/2 * 1/1
d= 3/2
d= 1 i 1/2
spr.
3d : 2 = 2 i 1/4
L = 3d : 2=3* 1 i 1/2 : 2= 3* 3/2 : 2= 9/2 * 1/2 = 9/4= 2 i 1/4
P = 2 i 1/4
2 i 1/4 = 2 i 1/4
L=P
b)
3 i 3/4 * 2x = 30
2x = 30 : 3 i 3/4
2x = 30 : 15/4
2x = 30 * 4/15
2x = 2 * 4/1
2x = 8/1
2x = 8
x = 8 : 2
x = 4
spr.
3 i 3/4 * 2x = 30
L= 3 i 3/4 * 2x= 15/4 * 2*4= 15/4 * 8 = 15/1 * 2= 30/1 = 30
P= 30
30=30
L=P
3a + 1 i 3/4 = 2 i 1/5
3a = 2 i 1/5 - 1 i 3/4
3a = 2 i 4/20 - 1 i 15/20
3a= 1 i 24/20 - 1 i 15/20
3a = 9/20
a = 9/20 : 3
a= 9/20 * 1/3
a= 3/20 * 1/1
a= 3/20
spr.
3a + 1 i 3/4 = 2 i 1/5
L= 3a + 1 i 3/4 = 3*3/20 + 1 i 3/4 = 9/20 + 1 i 15/20 = 1 i 24/20 = 2 i 4/20 =
= 1 i 1/5
P= 2 i 1/5
2 i 1/5 = 2 i 1/5
L=P
Szczegółowe wyjaśnienie:
