Which of the following equations does not have a solution in integers?

Solving each of the equations given.

A. x + 1 = 1

Taking 1 to RHS and subtracting from 1.

⇒ x = 1- 1

⇒ x = 0

The solution is an integer.

B. x – 1 = 3

Taking 1 to RHS and adding to 3.

⇒ x = 3+1

⇒ x = 4

The solution is an integer.

C. 2x + 1 = 6

Taking 1 to RHS and subtracting from 6

⇒ 2x = 6 – 1

⇒ 2x = 5

Now taking 2 to RHS and dividing 5

⇒ x = 2.5

The solution is not an integer.

D. 1 – x = 5

Taking 1 to RHS and subtracting from 5

⇒ -x = 5 – 1

⇒ - x = 4

Multiplying both the sides by -1

⇒ x = - 4

The solution is an integer.