Odpowiedź:
zadanie 10.
a)
1/3x - 2= x + 2
1/3x - x= 2 + 2
- 2/3x= 4
x= 4 : (-2/3)
x= 4 * (-3/2)
x= - 12/2
x= - 6
spr.
1/3x - 2= x + 2
L= 1/3x - 2= 1/3*(-6) - 2= - 6/3 - 2= -2 - 2= - 4
P = x+ 2= - 6 + 2= - 4
-4 = - 4
L=P
b)
1 - 6/7x = 4/7
- 6/7x= 4/7 - 1
- 6/7x= - 3/7
x= - 3/7 : (-6/7)
x= - 3/7 * (-7/6)
x= -1/1 * (-1/2)
x= 1/2
spr.
1 - 6/7x = 4/7
L= 1 - 6/7x= 1 - 6/7 * 1/2= 1 - 3/7 * 1/1 = 1 - 3/7 = 4/7
P= 4/7
4/7 = 4/7
L=P
c)
6(1/4x - 2) = 18
6*1/4x - 6*2 = 18
6/4x - 12= 18
3/2x= 18 + 12
3/2x= 30
x= 30 : 3/2
x= 30 * 2/3
x= 10 * 2/1
x= 20/1
x= 20
spr.
6(1/4x - 2) = 18
L= 6(1/4x - 2) = 6(1/4*20 - 2) = 6(1/1*5 - 2) = 6(5-2) = 6*3= 18
P= 18
18=18
L=P
d)
x/6 - 1/6 = 1 /*6 (mnożę stronami razy6)
6*x/6 - 6*1/6 = 6*1
x - 1 = 6
x= 6 + 1
x= 7
spr.
x/6 - 1/6 = 1
L= x/6 - 1/6 = 7/6 - 1/6 = 6/6 = 1
P = 1
1=1
L=P
e)
-2(2x - 1) = x/3
- 4x +2 = x/3 /*3 (mnożę stronami razy 3)
3 * (-4x) + 3*2 = 3* x/3
- 12x + 6 = x
- 12x -x = - 6
- 13x = - 6
x = - 6 : (-13)
x= - 6 * (-1/13)
x= 6/13
spr.
-2(2x - 1) = x/3
L= -2(2x - 1) = -2(2* 6/13 -1) = -2(12/13 - 1) = - 2*(-1/13) = 2/13
P = x/3= 6/13 : 3 = 6/13 * 1/3= 2/13 * 1/1= 2/13
2/13 = 2/13
L=P
f)
2/5(3 - x) = - 2
2/5 * 3 - 2/5x = - 2
6/5 - 2/5x = - 2
- 2/5x = -2 - 6/5
- 2/5x = - 2 i 6/5
- 2/5x= - 16/5
x= - 16/5 : (-2/5)
x= - 16/5 * (-5/2)
x= - 8/1 * ( - 1/1)
x= 8/1
x= 8
spr.
2/5(3 - x) = - 2
L= 2/5(3 - x) = 2/5(3 - 8) = 2/5 * (-5) = 2/1 * (-1) = - 2/1 = - 2
P= - 2
-2= - 2
L=P
g)
3/4(2 - 3x) = - 6
3/4 * 2 - 3/4*3x = - 6
3/2 * 1 - 9/4x= - 6
3/2 - 9/4x= - 6
- 9/4x = - 6 - 3/2
- 9/4x = - 6 - 1 i 1/2
- 9/4x = - 7 i 1/2
- 9/4x = - 15/2
x= - 15/2 : (-9/4)
x= - 15/2 * (-4/9)
x= - 5/1 * (-2/3)
x= 10/3
x= 3 i 1/3
spr.
3/4(2 - 3x) = - 6
L= 3/4(2 - 3x) = 3/4(2 - 3 * 3 i 1/3) = 3/4(2 - 3*10/3) = 3/4(2 - 1*10/1) =
= 3/4(2 - 10) = 3/4 * (-8) = 3/1 * (-2) = - 6/1= - 6
P = - 6
- 6= - 6
L=P
h)
1/5(x - 3) = 9 -x
1/5*x - 1/5*3= 9 - x
1/5x - 3/5= 9 - x
1/5x + x= 9 + 3/5
1 i 1/5x = 9 i 3/5
6/5x= 48/5
x= 48/5 : 6/5
x= 48/5 * 5/6
x= 8/1 * 1/1
x= 8/1
x= 8
spr.
1/5(x - 3) = 9 -x
L= 1/5(x - 3) = 1/5(8 - 3) = 1/5 * 5 = 1/1 * 1= 1
P = 9 - x= 9 - 8 = 1
1=1
L=P
i)
0,6 + x
------------- = x+1 /*2 (mnożę stronami razy 2)
2
""""""0,6 + x
2*--------------- = 2* x + 2*1
""""" 2
(z lewej strony równania 2 skracam z 2)
0,6 + x= 2x + 2
x - 2x = 2 - 0,6
-x = 1,4 /*(-1)
x= - 1,4
spr.
""""0,6 + x """""""0,6 - 1,4
L = ------------- = --------------- = - 0,8 : 2= - 0,4
"""""""2 """""""""""""2
P = x +1 = - 1,4 + 1 = - 0,4
- 0,4 = - 0,4
L=P
Szczegółowe wyjaśnienie:
