6th Class Mathematics Algebra Question Bank Algebra

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

A) \[x+1=1\]

B) \[x-1=3\]

C) \[2x+1=6\]

D) \[1\text{ }-x=5\]

Correct Answer: C

Solution :

(a) x + 1 = 1

\[\Rightarrow x+1-1=1-1\]

[Subtracting 1 from both sides]

\[\Rightarrow x=0\], which is an integer

(a) \[x-1=3\]

\[\Rightarrow x-1+1=3+1\]

[Adding 1 to both sides]

\[\Rightarrow x=4\], which is an integer.

\[\Rightarrow 2x+1-1=6-1\]

[Subtracting 1 from both sides]

\[\Rightarrow 2x=5\]

\[\Rightarrow \frac{2x}{2}=\frac{5}{2}.\] [Dividing both sides by 2]

\[\Rightarrow x=\frac{5}{2},\] which is not an integer.

(d) \[1-x=5\]

\[\Rightarrow 1-x-1=5-1\]

[Subtracting 1 from both sides]

\[\Rightarrow -x=4\]

\[\Rightarrow -(-x)=-4\]

[Multiplying both sides by (-1)]

\[\Rightarrow x=-4\], which is an integer.

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