Odpowiedź:
Poziom A
a) 3x + 7 + 2x = 22
3x + 2x = 22 - 7
5x = 15 /: 5
x = 3
Spr.: L = 3x + 7 + 2x = 3 • 3 + 7 + 2 • 3 = 9 + 7 + 6 = 16 + 6 = 22
P = 22
L = P
b) 8x - 5 - 4x = 15
8x - 4x = 15 + 5
4x = 20 /: 4
x = 5
Spr.: L = 8x - 5 - 4x = 8 • 5 - 5 - 4 • 5 = 40 - 5 - 20 = 35 - 20 = 15
P = 15
L = P
c) x - 9 + 7x = 55
x + 7x = 55 + 9
8x = 64 /: 8
x = 8
Spr.: L = x - 9 + 7x = 8 - 9 + 7 • 8 = 8 - 9 + 56 = -1 + 56 = 55
P = 55
L = P
d) 2x + 3 + 5x = 17
2x + 5x = 17 - 3
7x = 14 /: 7
x = 2
Spr.: L = 2x + 3 + 5x = 2 • 2 + 3 + 5 • 2 = 4 + 3 + 10 = 7 + 10 = 17
P = 17
L = P
e) 5x + 21 - 9x = 5
5x - 9x = 5 - 21
-4x = -16 /: (-4)
x = 4
Spr.: L = 5x + 21 - 9x = 5 • 4 + 21 - 9 • 4 = 20 + 21 - 36 = 41 - 36 = 5
P = 5
L = P
f) 6x - 23 - x = 7
6x - x = 7 + 23
5x = 30 /: 5
x = 6
Spr.: L = 6x - 23 - x = 6 • 6 - 23 - 6 = 36 - 23 - 6 = 13 - 6 = 7
P = 7
L = P
g) 4x - 19 + 2x = 23
4x + 2x = 23 + 19
6x = 42 /: 6
x = 7
Spr.: L = 4x - 19 + 2x = 4 • 7 - 19 + 2 • 7 = 28 - 19 + 14 = 9 + 14 = 23
P = 23
L = P
h) 7x + 6 - 5x = 24
7x - 5x = 24 - 6
2x = 18 /: 2
x = 9
Spr.: L = 7x + 6 - 5x = 7 • 9 + 6 - 5 • 9 = 63 + 6 - 45 = 69 - 45 = 24
P = 24
L = P
i) 9x + 12 - 3x = 18
9x - 3x = 18 - 12
6x = 6 /: 6
x = 1
Spr.: L = 9x + 12 - 3x = 9 • 1 + 12 - 3 • 1 = 9 + 12 - 3 = 21 - 3 = 18
P = 18
L = P
Poziom B
a) 5x = 3x - 6
5x - 3x = -6
2x = -6 /: 2
x = -3
Spr.: L = 5x = 5 • (-3) = -15
P = 3x - 6 = 3 • (-3) - 6 = -9 - 6 = -15
L = P
b) 8x = 14 + x
8x - x = 14
7x = 14 /: 7
x = 2
Spr.: L = 8x = 8 • 2 = 16
P = 14 + x = 14 + 2 = 16
L = P
c) 6x = 24 - 2x
6x + 2x = 24
8x = 24 /: 8
x = 3
Spr.: L = 6x = 6 • 3 = 18
P = 24 - 2x = 24 - 2 • 3 = 24 - 6 = 18
L = P
d) 7x = 3x - 4
7x - 3x = -4
4x = -4 /: 4
x = -1
Spr.: L = 7x = 7 •(-1) = -7
P = 3x - 4 = 3 • (-1) - 4 = -3 - 4 = -7
L = P
e) 4x = 28 - 3x
4x + 3x = 28
7x = 28 /: 7
x = 4
Spr.: L = 4x = 4 • 4 = 16
P = 28 - 3x = 28 - 3 • 4 = 28 - 12 = 16
L = P
f) 9x = 5x - 8
9x - 5x = -8
4x = -8 /: 4
x = -2
Spr.: L = 9x = 9 • (-2) = -18
P = 5x - 8 = 5 • (-2) - 8 = -10 - 8 = -18
L = P
g) 2x = 12 - 4x
2x + 4x = 12
6x = 12 /: 6
x = 2
Spr.: L = 2x = 2 • 2 = 4
P = 12 - 4x = 12 - 4 • 2 = 12 - 8 = 4
L = P
h) 3x = x + 10
3x - x = 10
2x = 10 /: 2
x = 5
Spr.: L = 3x = 3 • 5 = 15
P = x + 10 = 5 + 10 = 15
i) 5x = 3x - 12
5x - 3x = -12
2x = -12 /: 2
x = -6
Spr.: L = 5x = 5 • (-6) = -30
P = 3x - 12 = 3 • (-6) - 12 = -18 - 12 = -30
L = P
Pozdrawiam.
