Answer:
Proved
Step-by-step explanation:
Solving (a):
Let the numbers be: [tex]x, x + 1, x + 2.[/tex]
Their sum is:
[tex]Sum = x + x + 1 + x + 2[/tex]
Collect Like Terms
[tex]Sum = x + x + x + 1 + 2[/tex]
[tex]Sum = 3x + 3[/tex]
Divide sum by 3.
[tex]Result = \frac{Sum}{3}[/tex]
[tex]Result = \frac{3x+3}{3}[/tex]
[tex]Result = \frac{3(x+1)}{3}[/tex]
[tex]Result = x + 1[/tex]
Hence, this is true because there is no fractional part after the division
Solving (b):
Let the numbers be: [tex]x, x + 1, x + 2,x+3,x+4[/tex]
Their sum is:
[tex]Sum = x + x + 1 + x + 2+x + 3 + x + 4[/tex]
Collect Like Terms
[tex]Sum = x + x + x + x + x+1 + 2 + 3 + 4[/tex]
[tex]Sum = 5x+10[/tex]
Divide sum by 5.
[tex]Result = \frac{5x + 10}{5}[/tex]
[tex]Result = \frac{5(x + 2)}{5}[/tex]
[tex]Result = x + 2[/tex]
Hence, this is true because there is no fractional part after the division
Solving (c):
Let the numbers be: [tex]x, x + 1, x + 2,x+3[/tex]
Their sum is:
[tex]Sum = x + x + 1 + x + 2+x + 3[/tex]
Collect Like Terms
[tex]Sum = x + x + x + x + 1 + 2 + 3[/tex]
[tex]Sum = 4x+6[/tex]
Divide sum by 4.
[tex]Result = \frac{4x + 6}{4}[/tex]
Split
[tex]Result = \frac{4x}{4} + \frac{6}{4}[/tex]
[tex]Result = x + 1.5[/tex]
The 1.5 means that the sum can not be divisible by 4
