Gujarat BoardEnglish MediumSTD 6MATHSAlgebra1 Mark
MCQ
Which of the following equations does not have a solution in integers?
A
$x + 1 = 1$
B
$x - 1 = 3$
✓
$2x + 1 = 6$
D
$1 - x = 5$
✓
Answer
Correct option: C.
$2x + 1 = 6$
We know that, integers are
$-4, -3, -2, -1, 0, 1, 2, 3, 4$
Now, we check the equations.
For option $(a).$
$x + 1 = 1$
$\Rightarrow x = 1 - 1$ [transposing $+1$ to $RHS$]
$\Rightarrow x = 0,$ which is an integer.
For option $(b)$.
$x - 1 = 3$
$\Rightarrow x = 3 + 1$ [transposing $-1$ to $RHS$]
$\Rightarrow x = 4,$ which is an integer.
For option $(c)$,
$2x + 1 = 6$
$\Rightarrow 2x = 6 - 1$ [transposing $+1$ to $RHS$]
$\Rightarrow 2x = 5$
$\Rightarrow\frac{2\text{x}}{2}=\frac{5}{2}$ [dividing both sides by $2$]
$\Rightarrow\text{x}=\frac{5}{2},$ which is not an integer.
For option $(d)$.
$1 - x = 5$
$\Rightarrow -x = 5 - 1$ [transposing $+1$ to $RHS]$
$\Rightarrow -x = 4$
$\Rightarrow x = -4$, which is an integer. [dividing both sides by $-1$]
Hence, $(c)$ is correct option.
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