Question

Question 9

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) $1-x=5$

Answer 1

The set of integers include (..., -8, -7, -6,-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8,...)

$\begin{array}{ccc}\text{Equation}& \text{Solution}& \text{Integer (Yes/No)}\\ \left(a\right)x+1=1& x+1=1& \\ & x+1-1=1-1& \\ & x=0& Yes\\ \left(b\right)x-1=3& x-1=3& \\ & x-1+1=3+1& \\ & x=4& Yes\\ \left(c\right)2x+1=6& 2x+1=6& \\ & 2x+1-1=6-1& \\ & 2x=5& \\ & \frac{2x}{2}=\frac{5}{2}& \\ & x=\frac{5}{2}& No\\ \left(d\right)1-x=5& 1-x=5& \\ & 1-x-1=5-1& \\ & -x=4& \\ & x=-4& Yes\end{array}$

By analysing the table above, we can understand that the solution of the equation $2x+1=6$ is not an integer.