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Q.

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


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a

x+1=1

b

x-1=3

c

2x+1=6

d

1-x=5  

answer is C.

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Detailed Solution

It is given the equations.
(1) x+1=1 We can see that for x=0.
 0+1=1 Therefore, the value of x=0, satisfies equation and it is an integer.
So, option 1 is not correct.
(2) x-1=3 We can see that for x=4.  4-1=3 Therefore, the value of x=4, satisfies equation B and it is an integer.
So, option 2 is not correct.
(3) 2x+1=6 According to the question, lets assume x=1. So, (2×1)+1=3, which is not equal to 6. According to the question, lets assume x=2. So, (2×2)+1=5, which is not equal to 6. According to the question, lets assume x=3.
So, (2×3)+1=7, which is not equal to 6. Here, for x=3, the value of LHS 7 is more than the value of RHS 6  and for any value more than 3 the LHS will be bigger than RHS.
Also, there is no integer between 2 and 3 which gives a value of 2x+1=6.
Therefore, we can say that 2x+1=6, does not have a solution which is an Integer.
So, option 3 is correct.
(4) 1-x=5 We can see that for x=-4 1-x=1-(-4)=1+4 =5
Therefore, the value of x=-4, satisfies equation and it is an integer.
So, option 4 is not correct.
Hence, the correct option is 3.
 
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