Question

Which of the following could represent consecutive even integers?

a. x + 1, x + 2
b. x + 1, x + 3
c. 2x, 2x + 1

Answer 1

b. x + 1, x + 3

Explanation:

Integers : a number with no fraction part is called integers,

eg: ......-3, -2, -1, 0, 1, 2, 3......

Even integers : the integers which are multiple of 2.

Since, the difference between two consecutive even integers is always 2.

Eg : 2 and 4 are consecutive even integers.

⇒ 4 - 2 = 2.

∵ x + 2 - (x + 1) = x + 2 - x - 1 = 1,

x + 3 - (x+1) = x + 3 - x - 1 = 2,

2x + 1 - 2x = 1,

Hence, only x + 1 and x + 3 represent consecutive even integers

Answer 2

Only b. x+1, x+3 as long as x is an odd integer

a. x+1, x+2, wouldn't be consecutive even integers. If x is odd (e.g. 1), then 1+1=2 would be even but, 1+2=3 would be odd.

c. 2x, 2x+1, wouldn't be the answer. 2x will certainly be even but 2x+1 is going to be odd.