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

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x + 1 = 1

x - 1 = 3

2 x + 1 = 6

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)

2 x + 1 = 6

According to the question, lets assume

x = 1 .

So,

(2 \times 1) + 1 = 3

, which is not equal to

6 .

According to the question, lets assume

x = 2 .

So,

(2 \times 2) + 1 = 5,

which is not equal to

6 .

According to the question, lets assume

x = 3

.
So,

(2 \times 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

2 x + 1 = 6

.
Therefore, we can say that

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

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