Odpowiedź:
1)
2x + 7 = 6x +8
2x - 6x = 8 - 7
- 4x = 1
x = 1 : (-4)
x= - 0,25
spr.
2x + 7 = 6x +8
L= 2x + 7 = 2* (-0,25) + 7 = - 0,5 + 7 = 6,5
P= 6x + 8 = 6 * (-0,25) + 8 = - 1,5 + 8 = 6,5
6,5 = 6,5
L=P
2)
-3x + 4 = -9x + 15
-3x + 9x = 15 - 4
6x = 11
x= 11 : 6
x= 11/6
x= 1 i 5/6
spr.
-3x + 4 = -9x + 15
L= - 3x + 4= -3* 1 i 5/6 + 4= - 3* 11/6 + 4= -1 *11/2 + 4= - 11/2 + 4= - 5 i 1/2 + 4=
= - 1 i 1/2
P = - 9x + 15 = - 9 * 1 i 5/6 + 15= - 9 * 11/6 + 15= - 3 * 11/2 + 15= - 33/2 + 15=
= - 16 i 1/2 + 15= - 1 i 1/2
- 1 i 1/2 = - 1 i 1/2
L=P
3)
-6 - 4x = 15 - 6x
-4x + 6x = 15 + 6
2x = 21
x= 21 : 2
x= 10,5
spr.
-6 - 4x = 15 - 6x
L= -6 - 4x= -6 -4*10,5 = -6 - 42= - 48
P= 15 - 6x= 15 -6*10,5= 15 - 63 = - 48
-48 = - 48
L=P
4)
9 - 8x = 19 + 12x
-8x - 12x = 19 - 9
- 20x = 10
x= 10 : (-20)
x= - 0,5
spr.
9 - 8x = 19 + 12x
L= 9 - 8x= 9 - 8*(-0,5) = 9 - (-4) = 9 + 4= 13
P= 19 + 12x = 19 + 12*(-5) = 19 + (-6) = 19 - 6 = 13
13=13
L=P
5)
3(x + 9) - 2 = 22
3x + 27 - 2= 22
3x + 25 = 22
3x= 22 - 25
3x = - 3
x= - 3 : 3
x= - 1
spr.
3(x + 9) - 2 = 22
L= 3(x + 9) - 2= 3(-1 + 9) - 2= 3*8 - 2= 24 - 2= 22
P= 22
22=22
L=P
6)
4(5x + 7) + 5 = 41
20x + 28 + 5 = 41
20x + 33 = 41
20x = 41 - 33
20x= 8
x= 8 : 20
x= 0,4
spr.
4(5x + 7) + 5 = 41
P = 4(5x + 7) + 5 = 4(5*0,4 + 7) + 5= 4(2 + 7) + 5= 4*9 + 5 = 36 + 5= 41
P= 41
41=41
L=P
7)
-8(4 - 3x) + 12 = 92
- 32 + 24x + 12 = 92
24x - 20 = 92
24x = 92 + 20
24x = 112
x= 112 : 24
x = 112/24
x= 4 i 16/24
x= 4 i 2/3
spr.
-8(4 - 3x) + 12 = 92
L= -8(4 - 3x) + 12 = -8(4 - 3* 4 i 2/3) + 12= -8(4 - 3*14/3) + 12=
= - 8 (4 - 1 * 14/1)+ 12 = -8(4 - 14) + 12 = - 8 *(-10) + 12 = 80 + 12 = 92
P = 92
92 = 92
L =P
8)
5x + 3 + 4x = 8 + 15x + 4
9x + 3 = 15x + 12
9x - 15x = 12 - 3
- 6x = 9
x = 9 : (-6)
x = - 1,5
spr.
5x + 3 + 4x = 8 + 15x + 4
L = 5x + 3 + 4x = 9x + 3 = 9*(-1,5) + 3 = - 13,5 + 3 = - 10,5
P = 8 + 15x +4 = 15x + 12 = 15*(-1,5) + 12 = - 22,5 + 12 = - 10,5
- 10,5 = - 10,5
L = P
9)
7x - 4 - 2x = 6x - 12 - 10x
5x - 4 = -4x - 12
5x + 4x = - 12 + 4
9x = - 8
x = - 8 : 9
x = - 8/9
spr.
7x - 4 - 2x = 6x - 12 - 10x
L = 7x - 4 - 2x =5x - 4 = 5*(-8/9) - 4 = - 40/9 - 36/9 = - 76/9 = - 8 i 4/9
P = 6x - 12 - 10x = - 4x - 12 = - 4*(-8/9) - 12 = 32/9 - 108/9 = - 76/9 = - 8 i 4/9
- 8 i 4/9 = - 8 i 4/9
L=P
10)
6 - 11x + 19 = 4x - 7 + 3x
- 11x + 25 =7x - 7
- 11x - 7x = - 7 - 25
- 18x = - 32
x = - 32 : (- 18)
x = 32/18
x = 1 i 14/18
x = 1 i 7/9
spr.
6 - 11x + 19 = 4x - 7 + 3x
L = 6 - 11x + 19 = - 11x + 25 = - 11*1 i 7/9 + 25 = - 11 * 16/9 + 25= - 176/9 + 25=
= - 19 i 5/9 + 25 = 5 i 4/9
P = 4x - 7 + 3x = 7x - 7 = 7 * 1 i 7/9 - 7 = 7 * 16/9 - 7 = 112/9 - 7 =
= 12 i 4/9 - 7 = 5 i 4/9
5 i 4/9 = 5 i 4/9
L = P
Szczegółowe wyjaśnienie:
