Is this correct? Dividing integers? quick check?

Question

1) Write an expression in terms of an integer x for the sum of any 3 consecutive integers and show that this sum is divisible by 3

x + (x+1) + (x+2)

1 + (1+1) + (1+2)

1 + 2 + 3 = 6

6/3 = 2

2) Write an expression in terms of an integer x for the sum of any 4 consecutive integers and show that this sum is not divisible by 4

x + (x+1) + (x+2) + (x+3)

1 + (1+1) + (1+2) + (1+3)

1 + 2 + 3 + 4 = 10

10/4 = 5/2

Answer 1

x + (x+1) + (x+2)

=3x+3

=3(x+1)

that is , it is multiple of 3.

Hence it is divisible by 3

the value of x do not has to be 1

do the second in the same way

Answer 2

The person above is correct, but you cannot subsitute a number for x to prove that the terms will always be divisible by 3.  It is incorrect to do so because you may not be lucky with every number in another situation like this.

Answer 3

The question is not meant for you to substitute values in it.

Question #1:

Step 1: Find three consecutive integers.

x + (x+1) + (x+2) (<==very good!)

Step 2: Prove that these three integers are divisible by three.

x + (x+1) + (x+2)

x + x + 1 + x + 2 (<==combine like terms)

(x + x + x) + (1 + 2)

3x + 3

Step 3: Factorize this expression.

3x + 3

3(x+1)

Step 4: Divide by three.

3(x + 1)/ 3

(x + 1) • 3/3

(x + 1) • 1

(x + 1) (<==since the final outcome yielded an integer, we say that the sum of three consecutive numbers is divisible by three.)

Question #2.

This is much like the first one.

Step 1: Find four consecutive integers.

x + (x+1) + (x+2) + (x+3)

Step 2: Combine like terms

x + (x+1) + (x+2) + (x+3)

(x + x + x + x) + (1 + 2 + 3)

4x + 6

Step 3: Factorize.

4x + 6

2(2x + 3)

Step 4: Divide by four.

2(2x + 3) / 4

(2x + 3) • 2/4

(2x + 3) • 1/2

(2x + 3)/2 (<==Since the final outcome does NOT yield an integer, we say that four consecutive numbers are NOT divisible by four.)

Hope I helped!