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 x from the left side.


Note that because q is a constant, what that basically says is x(\text{some constant})=36.

Say for example the constant was 2. Then you’d have 2x=36 and that definitely has a nice clean integer solution. But even if the constant is something less neat and tidy, like \pi, \pi x= 36 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!

0x=36 simplifies to 0=36, 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 q that makes the constant -9+24q equal to zero. So let’s figure that out:


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