Rozwiązania w załącznikach.
Obliczenia do zadań:
Zadanie 1
a) x + 7 = 12 4 5 7
Sprawdzamy 4: Sprawdzamy 5: Sprawdzamy 7:
4 + 7 = 12 5 + 7 = 12 7 + 7 = 12
11 ≠ 12 12 = 12 14 ≠ 12
b) 6 = 2 - x 2 4 -4
Sprawdzamy 2: Sprawdzamy 4: Sprawdzamy -4:
6 = 2 - 2 6 = 2 - 4 6 = 2 - (-4)
6 ≠ 0 6 ≠ -2 6 = 6
c) 4(x - 2) = 0 -2 2 0
Sprawdzamy -2: Sprawdzamy 2: Sprawdzamy 0:
4(-2 - 2) = 0 4(2 -2) = 0 4(0-2) = 0
4*(-4) = 0 4*0 = 0 4*(-2) = 0
-16 ≠ 0 0 = 0 -8 ≠ 0
d) 3(x+1) = 9 2 3 -2
Sprawdzamy 2: Sprawdzamy 3: Sprawdzamy -2:
3(2+1) = 9 3(3+1) = 9 3(-2 + 1) = 9
3*3 = 9 3*4 = 9 3*(-1) = 9
9 = 9 12 ≠ 9 -3 ≠ 9
Zadanie 2
Sprawdzamy, które równania spełnia liczba 5:
3x - 10 = 5 5 - x = 0 5+5x = 10
3*5 - 10 = 5 5 - 5 = 0 5 + 5*5 = 10
15 - 10 = 5 0 = 0 5 + 25 = 10
5 = 5 30 ≠ 10
3 + 2x = 13 x - 5 = 2
3 + 2*5 = 13 5 - 5 = 2
3 + 10 = 13 0 ≠ 2
Sprawdzamy, które równania spełnia liczba 2:
10 = 5x 3 + 3x = 6 4x + 2 = 5x
10 = 5*2 3 + 3*2 = 6 4*2 + 2 = 5*2
10 = 10 3 + 6 = 6 8 + 2 = 10
9 ≠ 6 10 = 10
10x - 10 = 2 3x - x = 3
10*2 - 10 = 2 3*2 - 2 = 3
20 - 10 = 2 6 - 2 = 3
10 ≠ 2 4 ≠ 3
13 = 13
Sprawdzamy, które równania spełnia liczba -1:
6x + 6 = 0 5 - 2x = 7 10 + x = 11
6*(-1) + 6 = 0 5 - 2*(-1) = 7 10 + (-1) = 11
-6 + 6 = 0 5 - (-2) = 7 10 - 1 = 11
0 = 0 5 + 2 = 7 9 ≠ 11
7 = 7
9 = 9x 3x - 5 = 8x
9 = 9*(-1) 3*(-1) - 5 = 8*(-1)
9 ≠ -9 -3 - 5 = -8
-8 = -8
Sprawdzamy, które równania spełnia liczba -2:
3x + 2 = 4 2x - 4 = 0 6 - 2x = -5x
3*(-2) + 2 = 4 2*(-2) - 4 = 0 6 - 2*(-2) = -5*(-2)
-6 + 2 = 4 -4 - 4 = 0 6 - (-4) = 10
-4 ≠ 4 - 8 ≠ 0 6 + 4 = 10
10 = 10
4 - 2x = 8 7x = 14
4 - 2*(-2) = 8 7*(-2) = 14
4 - (-4) = 8 -14 ≠ 14
4 + 4 = 8
8 = 8
Zadanie 3
x - 3 = -2 x = -2
Sprawdzamy -2: Sprawdzamy 1: Sprawdzamy 3:
-2 - 3 = -2 1 - 3 = -2 3 - 3 = -2
-5 ≠ -2 -2 = -2 0 ≠ -2
3x - 8 = 1 x = 3
3*(-2) - 8 = 1 3*1 - 8 = 1 3*3 - 8 = 1
-6 - 8 = 1 3 - 8 = 1 9 - 8 = 1
-14 ≠ 1 -5 ≠ 1 1 = 1
5x + 3 = 8 x = 1
5*(-2) + 3 = 8 5*1 + 3 = 8 5*3 + 3 = 8
-10 + 3 = 8 5 + 3 = 8 15 + 3 = 8
-7 ≠ 8 8 = 8 18 ≠ 8
5 = 2x - 1 x = 3
5 = 2*(-2) -1 5 = 2*1 - 1 5 = 2*3 - 1
5 = -4 - 1 5 = 2 - 1 5 = 6 - 1
5 ≠ -5 5 ≠ 1 5 = 5
-5 = 2x - 1 x = -2
-5 = 2*(-2) - 1 -5 = 2*1 -1 -5 = 2*3 - 1
-5 = -4 - 1 -5 = 2 - 1 -5 = 6 - 1
-5 = -5 -5 ≠ 1 -5 ≠ 5
-2x - 3 = -5 x = 1
-2*(-2) -3 = -5 -2*1 - 3 = -5 -2*3 - 3 = -5
4 - 3 = -5 -2 - 3 = -5 - 6 - 3 = -5
1 ≠ - 5 -5 = -5 - 9 ≠ - 5
3x + 8 = -x
3*(-2) + 8 = -(-2) 3*1 + 8 = 1 3*3 + 8 = 3
-6 + 8 = 2 3 + 8 = 1 9 + 8 = 3
2 = 2 11 ≠ 1 17 ≠ 3
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Rozwiązania w załącznikach.
Obliczenia do zadań:
Zadanie 1
a) x + 7 = 12 4 5 7
Sprawdzamy 4: Sprawdzamy 5: Sprawdzamy 7:
4 + 7 = 12 5 + 7 = 12 7 + 7 = 12
11 ≠ 12 12 = 12 14 ≠ 12
b) 6 = 2 - x 2 4 -4
Sprawdzamy 2: Sprawdzamy 4: Sprawdzamy -4:
6 = 2 - 2 6 = 2 - 4 6 = 2 - (-4)
6 ≠ 0 6 ≠ -2 6 = 6
c) 4(x - 2) = 0 -2 2 0
Sprawdzamy -2: Sprawdzamy 2: Sprawdzamy 0:
4(-2 - 2) = 0 4(2 -2) = 0 4(0-2) = 0
4*(-4) = 0 4*0 = 0 4*(-2) = 0
-16 ≠ 0 0 = 0 -8 ≠ 0
d) 3(x+1) = 9 2 3 -2
Sprawdzamy 2: Sprawdzamy 3: Sprawdzamy -2:
3(2+1) = 9 3(3+1) = 9 3(-2 + 1) = 9
3*3 = 9 3*4 = 9 3*(-1) = 9
9 = 9 12 ≠ 9 -3 ≠ 9
Zadanie 2
Sprawdzamy, które równania spełnia liczba 5:
3x - 10 = 5 5 - x = 0 5+5x = 10
3*5 - 10 = 5 5 - 5 = 0 5 + 5*5 = 10
15 - 10 = 5 0 = 0 5 + 25 = 10
5 = 5 30 ≠ 10
3 + 2x = 13 x - 5 = 2
3 + 2*5 = 13 5 - 5 = 2
3 + 10 = 13 0 ≠ 2
Sprawdzamy, które równania spełnia liczba 2:
10 = 5x 3 + 3x = 6 4x + 2 = 5x
10 = 5*2 3 + 3*2 = 6 4*2 + 2 = 5*2
10 = 10 3 + 6 = 6 8 + 2 = 10
9 ≠ 6 10 = 10
10x - 10 = 2 3x - x = 3
10*2 - 10 = 2 3*2 - 2 = 3
20 - 10 = 2 6 - 2 = 3
10 ≠ 2 4 ≠ 3
13 = 13
Sprawdzamy, które równania spełnia liczba -1:
6x + 6 = 0 5 - 2x = 7 10 + x = 11
6*(-1) + 6 = 0 5 - 2*(-1) = 7 10 + (-1) = 11
-6 + 6 = 0 5 - (-2) = 7 10 - 1 = 11
0 = 0 5 + 2 = 7 9 ≠ 11
7 = 7
9 = 9x 3x - 5 = 8x
9 = 9*(-1) 3*(-1) - 5 = 8*(-1)
9 ≠ -9 -3 - 5 = -8
-8 = -8
Sprawdzamy, które równania spełnia liczba -2:
3x + 2 = 4 2x - 4 = 0 6 - 2x = -5x
3*(-2) + 2 = 4 2*(-2) - 4 = 0 6 - 2*(-2) = -5*(-2)
-6 + 2 = 4 -4 - 4 = 0 6 - (-4) = 10
-4 ≠ 4 - 8 ≠ 0 6 + 4 = 10
10 = 10
4 - 2x = 8 7x = 14
4 - 2*(-2) = 8 7*(-2) = 14
4 - (-4) = 8 -14 ≠ 14
4 + 4 = 8
8 = 8
Zadanie 3
x - 3 = -2 x = -2
Sprawdzamy -2: Sprawdzamy 1: Sprawdzamy 3:
-2 - 3 = -2 1 - 3 = -2 3 - 3 = -2
-5 ≠ -2 -2 = -2 0 ≠ -2
3x - 8 = 1 x = 3
Sprawdzamy -2: Sprawdzamy 1: Sprawdzamy 3:
3*(-2) - 8 = 1 3*1 - 8 = 1 3*3 - 8 = 1
-6 - 8 = 1 3 - 8 = 1 9 - 8 = 1
-14 ≠ 1 -5 ≠ 1 1 = 1
5x + 3 = 8 x = 1
Sprawdzamy -2: Sprawdzamy 1: Sprawdzamy 3:
5*(-2) + 3 = 8 5*1 + 3 = 8 5*3 + 3 = 8
-10 + 3 = 8 5 + 3 = 8 15 + 3 = 8
-7 ≠ 8 8 = 8 18 ≠ 8
5 = 2x - 1 x = 3
Sprawdzamy -2: Sprawdzamy 1: Sprawdzamy 3:
5 = 2*(-2) -1 5 = 2*1 - 1 5 = 2*3 - 1
5 = -4 - 1 5 = 2 - 1 5 = 6 - 1
5 ≠ -5 5 ≠ 1 5 = 5
-5 = 2x - 1 x = -2
Sprawdzamy -2: Sprawdzamy 1: Sprawdzamy 3:
-5 = 2*(-2) - 1 -5 = 2*1 -1 -5 = 2*3 - 1
-5 = -4 - 1 -5 = 2 - 1 -5 = 6 - 1
-5 = -5 -5 ≠ 1 -5 ≠ 5
-2x - 3 = -5 x = 1
Sprawdzamy -2: Sprawdzamy 1: Sprawdzamy 3:
-2*(-2) -3 = -5 -2*1 - 3 = -5 -2*3 - 3 = -5
4 - 3 = -5 -2 - 3 = -5 - 6 - 3 = -5
1 ≠ - 5 -5 = -5 - 9 ≠ - 5
3x + 8 = -x
Sprawdzamy -2: Sprawdzamy 1: Sprawdzamy 3:
3*(-2) + 8 = -(-2) 3*1 + 8 = 1 3*3 + 8 = 3
-6 + 8 = 2 3 + 8 = 1 9 + 8 = 3
2 = 2 11 ≠ 1 17 ≠ 3