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Question
The solution of which of the following equations is neither a fraction nor an integer.
Options
3x + 2 = 5x + 2
4x – 18 = 2
4x + 7 = x + 2
5x – 8 = x + 4
Solution
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.
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