Hey Mike! Is this a corresponding coefficients question? Can you solve please? Thanks! (#36 Section 4)

-9x + 24qx = 36

In the given equation, q is a constant. The equation has no solution. What is the value of q?

It’s not really a corresponding coefficients question, though maybe you could argue it’s a cousin of those. It’s really a question testing whether you know what it means for an equation to have no solution. Tricky!

Let’s factor out from the left side.

Note that because is a constant, what that basically says is .

Say for example the constant was 2. Then you’d have and that definitely has a nice clean integer solution. But even if the constant is something less neat and tidy, like , still has a solution, it’s just less pretty.

What’s the only time when the equation *won’t* have a solution?

When the constant equals zero!

simplifies to , which is not true, which would mean there is no solution. Since we *want* no solution to be able to answer this question, we’re really looking for the value of that makes the constant equal to zero. So let’s figure that out: