Question

In the following equation, a and b are integers.2x + a = 5 + bx What value of b would make the equation have no solutions?

Answer 1

Notice that if we make b = 2,

$\begin{gathered} 2x+a=5+bx \\ \rightarrow2x+a=5+2x \\ \rightarrow a=5 \end{gathered}$

a would have to be 5 in order for the equation to have solutions at all. But if a is not 5, then the equation has no solutions

Answer: b = 2