Question

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

Options

• x + 1 = 1

• x – 1 = 3

• 2x + 1 = 6

• 1 – x = 5

Answer 1

2x + 1 = 6

Explanation:

(A) x + 1 = 1

⇒ x + 1 – 1 = 1 – 1 ...[Subtracting 1 from both sides]

⇒ x = 0, which is an integer.

(B) x – 1 = 3

⇒ x – 1 + 1 = 3 + 1 ...[Adding 1 to both sides] 

⇒ x = 4, which is an integer.

(C) 2x + 1 = 6

⇒ 2x + 1 – 1 = 6 – 1 ...[Subtracting 1 from both sides]

⇒ 2x = 5   

⇒ `(2x)/2 = 5/2`  ...[Dividing both sides by 2]

⇒ `x = 5/2`, which is not an integer.

(D) 1 – x = 5

⇒ 1 – x – 1 = 5 – 1  ...[Subtracting 1 from both sides]

⇒ –x = 4

⇒ –(–x) = –4  ...[Multiplying both sides by (–1)]

⇒ x = –4, which is an integer.

Thus, the above conditions show that equation 2x + 1 = 6 does not have a solution in integers.