Question

Px - 17 = 22 + Qx find the values of P and Q so that the equation has no solution

Answer 1

First, we must combine similar terms. If we move -17 to the right hand side as +17 and Qx to the left hand side as -Qx, we obtain,

`Px-Qx\questeq22+17`

if we factorize x, we obtain

`(P-Q)x=39`

We can see that the equation has no solution if we obtain a contradictory result.

For instance, if P is equal to Q, we have

`\begin{gathered} 0\cdot x=39 \\ \sin ce\text{ 0 times x is zero, we have} \\ 0=39\text{ !!!} \end{gathered}`

which is an absurd result. Then, if P = Q the equation has no solution for any x