Question

If x represents a whole number, then which of the following expressions can represent any positive odd integer?

• A. $2x+1$
• B. $2x$
• C. $x+1$
• D. $3x+4$

Answer 1

The correct option is A

$2x+1$

An odd number is a number which is one more than, or one less than an integral multiple of $2$

For example, $3$ is an odd number.

3 can be written as

$2\times 1+1$

( $2\times 1$ is an integral multiple of $2$ here)

So, no matter what whole number $x$ represents, either $2x+1or2x-1$ represents an odd integer.

When $x=0,2x-1=2\times 0-1=-1$

$-1$ is not a positive number.

Hence, the expression $2x-1$ cannot always represent a positive odd integer.

Thus, when $x$ is a whole number, $2x+1$ is always a positive odd integer.