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: 