The solution of which of the following equations is neither a fraction nor an integer?

Let us solve the equations:

(a). Given equation is 2x + 6 = 0

⇒ 2x = –6 [transporting 6 to RHS]

⇒ [Dividing both sides by 2]

⇒ x = –3 (integer)

(b). Given equation is 3x – 5 = 0

⇒ 3x = 5 [transporting 5 to RHS]

⇒ [Dividing both sides by 3]

⇒ (fraction)

(c). Given equation is 5x – 8 = x + 4

2⇒ 5x = x + 4 + 8 [transporting 8 to RHS]

⇒ 5x = x + 12

⇒ 5x – x = 12 [transporting x to LHS]

⇒ 4x = 12

⇒

⇒ x = 3 (integer)

(d). Given equation is 4x + 7 = x + 2

⇒ 4x = x + 2 – 7 [transporting 8 to RHS]

⇒ 4x = x – 5

⇒ 4x – x = –5 [transporting x to LHS]

⇒ 3x = –5

⇒

⇒ (neither a positive fraction nor an integer)