1) First integer = x
Second integer = x + 1
Third integer = x + 2
Sum of the three consecutive integers = 0
Equation:
x + (x+1) + (x+2) = 0
3x + 3 = 0
3x = 0 - 3
3x = -3
3x/3 = -3/3
x = -1
Substitute -1 for x:
First integer: x = -1
Second integer: x + 1 = -1 + 1 = 0
Third integer: x + 2 = -1 + 2 = 1
The three consecutive integers are -1, 0, and 1
Check:
-1 + 0 + 1 = 0
0 = 0
2) First odd integer = x
Second odd integer = x + 2
Third odd integer = x + 4
Fourth odd integer = x + 6
Fifth odd integer = x + 8
Sum of the five consecutive five integers = 66
Equation:
x + (x+2) + (x+4) + (x+6) + (x+8) = 55
5x + 20 = 55
5x = 55 - 20
5x = 35
5x/5 = 35/5
x = 7
Substitute 7 for x:
First odd integer; x = 7
Second odd integer: x + 2 = 7 + 2 = 9
Third odd integer: x + 4 = 7 + 4 = 11
Fourth odd integer: x + 6 = 7 + 6 = 13
Fifth odd integer: x + 8 = 7 + 8 = 15
The five consecutive odd integers are 7, 9, 11, 13, 15.
Check:
7 + 9 + 11 + 13 + 15 = 55
27 + 28 = 55
55 = 55
