Question

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

विकल्प

• 3x + 2 = 5x + 2

• 4x – 18 = 2

• 4x + 7 = x + 2

• 5x – 8 = x + 4

Answer 1

4x + 7 = x + 2

Explanation:

a. Given linear equation is 3x + 2 = 5x + 2

⇒ 3x – 5x = 2 – 2  ...[Transposing 5x to LHS and 2 to RHS]

⇒ –2x = 0

⇒ `(-2x)/(-2) = 0/(-2)`  ...[Dividing both sides by –2]

∴ x = 0

Hence, x = 0 is an integer.

b. Given linear equation is 4x – 18 = 2

⇒ 4x = 2 + 18  ...[Transposing –18 to RHS]

⇒ 4x = 20

⇒ `(4x)/4 = 20/4`  ...[Dividing both sides by 4]

∴ x = 5

Hence, x = 5 is a positive integer.

c. Given linear equation is 4x + 7 = x + 2

⇒ 4x – x = 2 – 7  ...[Transposing x to LHS and 7 to RHS]

⇒ 3x = –5

∴ `x = (-5)/3`   ...[Dividing both sides by 3]

Hence, `x = (-5)/3` is neither a fraction nor an integer.

d. Given linear equation is 5x – 8 = x + 4

⇒ 5x – x = 4 + 8   ...[Transposing x to LHS and – 8 to RHS]

⇒ 4x = 12

⇒ `(4x)/4 = 12/4`  ...[Dividing both sides by 4]

∴ x = 3

Hence, x = 3 is a positive integer.

From the above it is clear that, 4x + 7 = x + 2 satisfies the condition.