Question

Prove without solving that the solution of the equation 7(2x+1)=13 is not a whole number.

Answer 1

Assume x is a whole number. Then 2x+1 is a whole number, and 7(2x+1) is a whole number that is a multiple of 7.

13 is not a multiple of 7, so we have reached a contradiction, and our assumption must be false.

x cannot be a whole number.